Like all media telling a story, characters in video games require detail and definition - especially player characters. It's not just the gameplay mechanics that make up your digital avatar; exploration into interesting costume design, back story, dialogue/voice acting and even animations go towards making your avatar identifiable and worthy of emotional investment. It's what puts Nathan Drake miles apart from Duke Nukem when mechanically they're just means to an artillery.
However, the range of backgrounds in video game protagonists is still rather limited, when compared to books or film. While there are all different kinds of 'noble hero' characters (often falling into the majority demographic of straight, white and male) - differing in body type and personality; minority protagonists are a lot more uncommon. A black player character is rather anomalous - and have fun thinking of 5 or more protagonists who aren't straight.
Having recently observed the problematic train wreck (link is NSFW) that was Duke Nukem Forever, and the recent decision to have the female version of Commander Shepard as the main face of Mass Effect 3, I feel a lot more aware of women in protagonist roles. While they're not uncommon (an RPG without any kind of woman party member would be incredibly strange); whether they're handled well and varied is another matter.
She's cool, capable, and her battle armour doesn't fall into the stereotypical design flaws of having 'boob-plate', or an exposed midriff. On the other hand, she comes across as incredibly personality-deprived. While the very early games get an excuse in a lack of scope in animation or dialogue, with the suit on, Samus may as well be a robot - though once the suit comes off, she is suddenly svelte and sassy.
The rendition of Samus in Metroid: Other M is much worse, though the approach is different. Samus is much more notably female in her animations without sacrificing her armour style or fighting prowess. On the other hand, the attempt at giving her dialogue ended up veering wildly from what minimal original characterisation she had - suddenly losing some of her 'lone wolf' attitude, and a ham-fisted attempt at creating character relations with her commander instead came across as supplicant to a fault. My personal favourite rendition of Samus would be her appearance in Super Smash Bros. Brawl. The game's story mode is without dialogue; meaning Samus' personality is portrayed entirely through her actions, and it's handled quite well for something arguably throw-away.
Jade stands out as my personal favourite example of a great woman protagonist. It manages to straddle a thin line of a character having markedly (though socially assumed) feminine traits, but those traits not being the driving force behind everything she is. She has a motherly trait in her taking care of orphans, she wears make-up, and she is by no means unshapely; but her practical fashion reflects the action-oriented work she does, she's a charismatic leader without relying on her figure, and she's sure of herself and her goals. Her partner characters are both male (one of whom ticks all the buttons for 'brave masculine protagonist'), but they both treat her with respect (though could you imagine what the gameplay would be like if they didn't?). What stops Jade from being perfectly well-rounded is her lack of flaws. Hyper-competence is almost always going to be a factor of a playable character; but Jade's actions and interaction are unwaveringly 'the right thing to do'; somewhat ironic, considering the game title.
BG&E reminds us that the key to great characterisation is not avoiding all tropes that are part of a stereotype; but using those aspects in conjunction with other, maybe even contrasting elements to bring about someone well-rounded and likeable. Just don't be afraid to add character flaws.
Design-wise, this has lead to Bayonetta being very specifically designed as fetish-bait. As her clothes are made from her enchanted hair, whenever a Wicked Weave attack is performed (which will be often, if you're playing well), her clothing gets a lot skimpier. Her proportions are entirely inhuman - accentuating legs and waist with a tiny head - why would you need to be looking at her expression when you could be looking at her ass? Everything is delicate and feminine, from the lipstick-shaped lock-on reticule to the way the damage Bayonetta takes results in explosions of rose petals and butterflies. There's nothing intrinsically wrong with that direction, but its inclusion feels condescending, like nothing else would suit a woman in an action role. (It's something that also has me worried about Lollipop Chainsaw...)
On the other hand, someone on the design team realised that the character would be dead in the water if she remained nothing but a long-legged sex doll; and the gameplay and story make a good attempt to keep the pandering to a less-pervasive level. During combat, the camera is barely focused on Bayonetta herself - the game takes its battles very seriously, and is designed so attention is drawn to incoming attacks and vulnerability animations, not gyrating witch-butt. The attacks and taunts designed for showing off are actually incredibly unsafe, and the game has no qualms about sending a swift death your way if you mess about. The storyline has surprisingly little dialogue-focus on Bayonetta's assets and attitude (the camera angles do the dirty work instead), and gives Bayonetta as a character the room to grow a little. By the end of the game her attitude of selfishness and hedonism has opened up into something more caring, without losing her independence.
It feels as if the character of Bayonetta in the game and Bayonetta in cut-scenes were designed by two different people. The silent sexy dancing of the credits and against other female rivals lie in stark conflict with the flippant foul-mouthed stance she takes almost everywhere else. There have been hints at a sequel from Platinum Studios - hopefully they'll find something more to do with Bayonetta's character beyond her sexuality and love of violence.
However, it feels like they take those raw concepts, and come out with something a lot angrier. With a past like the one Purna was given, bitterness is bound to be expected, but here it's resulted in the polar opposite of the 'extra-feminine, demure and pure' stereotype - a 'cold, rage-fuelled uberfeminist' stereotype which, in practice, ends up being just as tasteless. It still boils down to an easily dismissed character, not because she's weak, but because she's too aggressive, her power being focused not on her self and in her own abilities, but in hating others, and particularly in hating men. The biography does not outright call her man-hating, but the game mechanics bear more information.
One of Purna's abilities is called "Gender Wars", which allows her to deal bonus damage to male targets. A little off-kilter, but the punchline comes in when, in the initial release of Dead Island on Steam, one purchaser decided to look at the game code, and found that the code named the ability as "Feminist Whore". Whoops. Developers Techland since altered the code in later releases, and put out a press release saying that the coder who wrote that part of the program would be reprimanded; but it makes me wonder how deeply the attitude of 'Purna the Feminist Whore' was entrenched in the design process for the character. Like with Bayonetta, the intents and attitudes of the creator are hard to separate from the finished product, even if alternate interpretations are less problematic.
The scope of character design is massive - the potential for protagonists in games is just as large as in novels or in films, but it will take a concentrated effort from games designers to acknowledge the potential for minority player characters in their work; and well-rounded characters in general. It's not impossible to form an empathy with a character who isn't the same gender, race or sexuality as you, so tailoring character design to demographic majority would be outdated and unnecessary. However, creating an identifiable player character in the first place can be a very demanding task, so the popularity of games where the looks of the protagonist are chosen by the player makes sense. Women are getting a wider and more balanced representation as the heroes of video games; though the number of them that end up in DD Breastplate and bikini-mail need to be worked on.