There's nothing wrong with female characters, with original characters, with fantasy powers, with unusual names and physical characteristics, with plots revolving around a "chosen one," with complicated and dark backstories, with characters who are exceptional in one or even a select few compatible fields, or with romantic subplots up to and including love triangles.
The problem comes when the author doesn't pull any of those off.
1) Avoid implausibility.
One of the quickest ways to improve the quality of your characterization is to get rid of the notion that "unique" powers, physicality, names, and other trivia constitute characterization. Keeping in mind that, according to Mark Twain, Filling out a character sheet with a character's scars, height, and favorites, while useful for your own information, is not a valid exercise in characterization either. The fact that your heroine has blue hair has absolutely no impact on her actions, her thoughts, or how the audience feels about her.
The absolute most important test of having a good character with an individual personality is to ask yourself, in any situation where it applies, "what would x do?" When you've reached the point that you are not only confident in what your knight in shining armor or your priestess of the mother goddess would do, but why they would do it, you're ready to write about them and perhaps have it read, not before.
Make your characterization consistent, and make sure that you only pick a select few, extremely plot-important things, that they need to have or be able to do in order for the plot to eventuate. Cut out any and all attributes that exist solely to make them not look or act like other people in their same species, hometown, ethnic group or whatever. Check that any alterations they make to their appearance, as well as anything you've decided to make them wear or own, are actually attainable in the place where they live (with no excuses about how "it's rare, but her merchant uncle brought it from x," because if the uncle was a merchant, he'd be more likely to try and sell it,) as well as being appropriate for the activity. If you can, field-test articles of clothing by seeing how well you can walk in high heels, how fast you can run in a narrow skirt, or how easy it is to carry around a sword-length item. Also, outfits in the real world – as in, the world where any labor, experimentation, or serious hiking is done, rather than the insulated modern world of your school and jobs – are chosen because they protect the wearer from the hazards of their workplace, rather than because they show specific amounts of skin. If I read about one more smith pounding up a storm of sparks in his smithy, rippling-muscled and shirtless, I'll stick you in a real smithy. I hear there's one at your local renaissance faire or annual reenactment.
Reality checking your character's strength and dexterity versus their height, weight, and muscle mass is another thing you need to do. You can have a heroine who is five five and only weighs one hundred pounds, but she will not be strong enough to lift a broadsword. I'll be surprised if she manages a backpack with a couple of textbooks, actually, because that's not a healthy weight for her height. And for the sake of your sanity and mine, when you are trying to find what's a healthy weight for your heroes and heroines, use a chart from a medical site, rather than one that is simply floating about online: most of those are wildly inaccurate.
Check the protagonist's actions for plausiblility too. If you have a sixteen-year-old skinny wimp, he's going to have a lot more trouble carrying damsels out of distress than the football linebacker. Likewise, having a tiny 5'1" fairy-girl carry the 5'11" wounded action hero out of danger so that she can heal them becomes quite laughable.
2) Avoid trying to do too much in too little time.
This is a common flaw in planning as well as one of the lead reasons for having underdeveloped plot and secondary characters. If you have a character who is an exotic hybrid of two or more species, has several key skills, one or more of which is of paramount importance to the plot, has two love interests and an admirer who they simply don't think of that way, a classroom full of friends or devoted followers, a serious problem with mouthing off to authority, dead parents, emotionally abusive adoptive parents, a hospitalized little sister, and the ability to take down up to ten armed mooks, you're going to have a very, very hard time showing all that in a few thousand words. People who try to cram all of that into one character end up with most of the character's attributes being informed characteristics, and therefore unrealistic and boring to the audience, as well as little to no development of secondary characters. At best, you have a story where there are no notable characters besides your hero or heroine. At worst, you have a story where every single character exists to praise your main character, attack them, or be inexplicably jealous of them for qualities that we have never observed in the wild.
Instead, narrow what you show of your character to just the traits which are actually important to the main plot. Show in the action that your character is highly skilled without ever telling us instead. Throw out things that are implausible or tone them down – instead of being a hybrid of multiple alien species, if their heritage isn't a pivotal plot point, make them merely cross-cultural. Don't focus on their random likes, dislikes and physical appearance unless there is a compelling, plot-related reason to do so. (Eg: you actually like red peppers, you can't be Stacy! She hates them! You're an impostor!)
Feel free to prune side-plots, especially clichéd ones like love triangles and finding out that the main character's parents aren't who they think that they are. Remember how long you are going to be writing this: for five thousand words, or for five hundred thousand words?
Incidentally, you can have story elements that are not introduced right away, or which you don't tell us at all. Perhaps the main character's motivation for becoming a bounty hunter is to pay for an operation which will allow her hospitalized little sister to walk again. This little sister is not biologically related to her, but the character does not know that, because her controlling and manipulative adoptive parents never told her about her mother and father, who died in a freak accident when she was two, and have spent the last twenty years trying to keep both girls under their thumbs. A backstory like this should not be summed up in a handful of paragraphs and then forgotten. Show your character aggressively going for the biggest rewards, squirreling away every last cent, disappearing for hours. Later you can reveal to the audience that the reason she disappears is to go visit her sister, preferably after some other action, such as the collection of a few bounties, has taken place. This not only builds suspense, but credibility. If you construct your story carefully, foreshadowing events enough that they don't appear to have been tacked on whenever you need them, and revealing new developments slowly, you're more likely to preserve your audience's suspension of disbelief.
3) Spend time on other characters.
Yes, your main character is important. But in nine cases out of ten, not paying enough attention to them is not the source of the problem. The problem of characterization that leads to the other characters acting as if their sole purpose in life is to revolve around the main character is that you haven't given them anything else to do.
Any character that is going to be in the whole book – or at least every time the protagonist is in a certain group of situation (i.e. school, the rebel camp, parties held by the nobility,) needs to be developed. The same goes double for family members and supposed good friends of the main character, as well as any personalities they happen to go on a random quest with. In order to do this, you need to spend some time making sure that these characters have some significant relationships that your main character isn't involved in, their own opinions, and their own ways that they spend downtime, at the very least.
For example, if you are spending your half hour developing the main heroine's mother, you need to examine how she relates to the heroine's father, (and to her husband, should he not be the same person,) what she really thinks of her daughter, how she relates to any other offspring she may have, and to people who don't play significant roles in the heroine's life, like extended family members and adult neighbors. In addition he needs to have an opinion on something that is not related directly to her daughter – for example, she might think that the farmer down the road is a tight-fisted miser. As long as she doesn't develop this opinion because he overcharged her heroine daughter for eggs, or because he was rude to the precious young protagonist, this counts. Think of at least three things that she has an opinion on which do not directly relate to her daughter. Then, at some point during the conversations she will inevitably have with her daughter, other family members, or neighbors, make her state her opinions. When and how she states them (does she only state them where others of the same opinion will back her up, or does she address the miserly farmer directly?) will give you a bare minimum of characterization that makes this woman more than a plot device for giving birth to your heroine, changing her diapers, and feeding and housing her for the last something-teen years.
As far as love interests go, you should develop them almost as extensively as the main character. We need to see not only why they fall in love with the heroine ("She's the most gorgeous woman in the world," is not sufficient excuse,) but have an extensive list of how they feel about other things. And developing his opinions, his family, his childhood, his experiences, and even his little pet peeves gives your romantic couple something to quarrel realistically about, so you don't need to rely on the idiot plot of each thinking that the other is cheating on them for no good reason. Instead, you could have them fight because he always leaves the seat up, and your heroine is sick of midnight bathroom-breaks ending with her derriere in the loo. Not every fight has to be relationship –breaking either, while we're at this topic, which brings us to the next point.
4) Romance: how to make the other half of the relationship more than a human accessory.
The thing about romance in fiction is that it comes up a lot, partly due to the fact that modern culture is highly sexualized, and partly due to the fact that fiction necessarily contains a lot of wish-fulfillment. A steady romantic partnership is a pretty common wish for a lot of the writer and readership.
The type of relationship doesn't have to be a cookie-cutter version of "twu wuv," however. In addition to there being many more variations of romance and sexuality (some of which are not necessarily connected,) than most people seem to account for by labeling their characters straight, gay, or bi, there's also the fact that relationships take a lot more work than many writers seem to want to record. At best, this kind of authorial laziness gives us improbable hookups in which the duo are supposed to be "soulmates" because of a combination of having great sex, some sort of destiny or prophecy, or because one or both are part of a magical species that recognizes it's other half on sight, smell, or the convenient and magical appearance of empathy powers, strange skin markings, heightened senses or whatever in the formerly ordinary partner.
In real life, people date. People start relationships for plenty of reasons: they ask someone pretty out on a date, they realize that they feel very safe and happy with a longtime friend or coworker, they get set up by friends, or any number of other reasons. They also end relationships for a variety of reasons: not having the same goals, needing to separate geographically, finding out that they don't have much in common with the other person besides the sex, not being attracted to the other person anymore (or maybe not having been in the first place) or because they don't feel ready for commitment. Sometimes this happens after people have been married for years.
So why are fictional relationships overwhelmingly portrayed as being either completely good - with twu wuv, jumping in the sack like bunnies, no disagreements, bushels of roses, and sipping the same milkshake out of two straws – or completely bad, with the non-protagonist member being abusive, argumentative, controlling, and cruel? In many stories I've read, this 'abuse' by the other partner is used as a justification for the hero or heroine (it often is a heroine,) to either leave them or jump in bed with someone else and have an affair.
Too often as well, the supposedly ideal relationships are stereotypical and lifted directly and badly from the idealized couple of the 1950's, with their white picket fence and father knows best. Sometimes authors decide to go the Pride and Prejudice route instead, but they tend to mistake bickering about everything for sexual tension. Neither of these routes towards a relationship will work with every couple, especially when they are applied haphazardly. If you intend to give your character a stable and lasting relationship, there needs to be a period of getting to know the other character, discovering what each partner believes, what they agree and disagree on, and why they respect each other. And in order to do this well, you have to do it slowly.
If the only reason the two are together at all is that she's the most beautiful maiden in the world and he's the strongest knight, I'm going to assume that they're only having a one-night stand. Even if it results in marriage (nothing wrong with having the girl's daddy pull out the shotgun and take them to the local church,) no one is going to buy that this partnership is true love, especially when they spend their wedding night with nothing to talk about.
Alternatively, have their relationships not be true love or absolutely horrible. If your characters have been betrothed since childhood, perhaps their partnership isn't about simmering passion, but a civil and political relationship where both the man and the woman have roles to play in running a castle and raising children, and where they become fond of each other. Or perhaps a marriage in which they respect each other, but spend an excessive amount of time apart and only have sex in order to try for an heir. Perhaps you could have a protagonist who marries her high school sweetheart and then, two kids and ten years later, decides to get a degree because she's tired of standing behind the white picket fence. Maybe she fights with her hubby about money and how they should save or spend it, about how they should discipline the kids, about the in-laws that so many authors ignore. Maybe they even go to bed angry a few times, and make it up when they both realize that they're being stubborn.
5) Sex and stereotypes.
Your character's attitude towards sex will depend on their era, the way they were raised, their own personal opinions, and their own experience. Their attitude towards their gender and sexual preferences will come from the same list. One of the most annoying ways to sidetrack a character is to make them either implausibly liberal for the setting in regards to sex, or extraordinarily virginal. (Victorian era heroines in particular, when written by modern authors, are guilty of this, professing to their mothers and dowager aunts that they will marry for love, and letting their sweethearts into their boudoirs. Unless, that is, they're so virginal that they blush at the sight of a man's undone collar – this modesty only lasts until their more experienced lover has had a roll in the hay with them and magically makes their first time extra-special and, illogically, completely free of pain or confusion.)
Now, in some settings (say, if your protagonist was raised in a monastery or nunnery,) it is plausible for them to be extremely virginal, just as it's plausible for them to be sleeping about if they're a twenty-something year old attending Woodstock. The problem is when their behaviors and attitudes reflect the author meddling with their opinions more than the way they would logically have been raised, given the personal beliefs of their parents or other caregivers, and the social mores of the time. The same is true of gender, and while it is true that the women's rights movement dramatically changed the conception of women's role in society in the space of a few short generations, there are always some connections between the way a child was raised and the way they view themselves as adults, even if they don't consciously realize it.
A special note on gay and lesbian couples; one does not have to be the "man" in the relationship, nor does the other have to be the "woman." You can successfully pair two stereotypically manly men or two stereotypically feminine girls, if you take a good think about how the parts of their relationship dealing with respect and companionship work, instead of relying on cliché indicators of romance. Instead of holding doors for each other, perhaps your men like to go out deerhunting and sit in the cabin with a pair of beers after that, and perhaps your young ladies demonstrate their affection by being curled up on the couch painting each other's toenails. Being friends first and lovers second doesn't have to apply strictly to heterosexual couples as a recipe for a stable relationship.
Not making your character fall in love, or have sex with, every member of the correct gender and orientation that they meet is an excellent way to keep the story plausible, and to make sure that other plot threads get due consideration. And being prepared to address a character who never gets any action, one who is in an unfulfilling relationship that's mostly about the sex, or a character who is conducting an intense, platonic relationship via letters, or perhaps even a character who just doesn't see what the big deal about sex is can cause drastic improvements to the range and depth of characters that you're prepared to write.