To begin with, let us lay down some ground-rules. These are like the fundamental laws of physics.
1. All laws are mutable.
2. None of this is concrete.
3. Characters are defined as actors in a video game or other media which have human or psudeo-human emotions at least once. Machines are, therefore not counted as characters, with the exception of self-aware, or semi-self aware machines.
4. Personality is made by reaction as much as it is action.
5. Characters have life before and (unless dying en-route) after the time-span of the game.
6. Characters exist in a universe/reality together and therefore interact, both with each other and the reality around them.
7. Said interactions are the definition of the storyline in any decent experience (game or novel, or what have you).
8. Villains are characters, too.

This is a very important part, because it defines how the game will be played. A game in a dystopian society being ruled by a merciless overlord looks, acts, and reacts differently than a utopia slowly crumbling into chaos. It also defines the weapons, items, technology, magic, etc, that are used. I would heavily discourage cliche`d worlds (Might and Magic sort of things, valiant hero fighting supreme evil) unless you really have a good spin to it. Speaking of which.
-Spin
Spin is a way of taking a theme or idea and changing the way it looks, acts or works. Good ways of dong this are to combine more than one theme or idea, to produce a hybrid, or to carefully mix a few ideas together. An example would be taking a fantasy world and replacing the magic with steam-punk technology(or high technology, for that matter), or combining the magic with technology.

The world includes the cultures, races and ethnicities of the life-forms in the game, and their ensuing interaction. sometimes this interaction can be an overlying theme for the whole, such as two races/cultures locked in war.

The world also includes...

Honestly this idea is so played out I avoid it like the plague, with few exceptions.
But.
Monsters can be natural (man-eating tigers are common in the wilds of Asia), they can be fantastic (Natural animals that do not exist (no magic powers)), or they can be magical. they should fit thematically and otherwise in a story (a Kraken in a mountain makes no bloody sense).

Finally we get to the meat...

this is the tough one, cause you want a unique character, that is likable and everyone can identify with. The best way, I've found to do this is to use Contrast, Depth, and Personal Detail.

Contrast can be achieved by doing such things as having a very loud, annoying, and rude actor be a great assassin, or some such similarity. It also is achieved in clothing, and even the other characters said actor is paired with. (the rival this working together is very outplayed...avoid it.)

Depth this is a characters past, and his/her emotions. This is for the writers in the crowd, giving a character depth is a difficult process, especially giving them a unique variety of depth. Deep characters have plans, ideals, morals, and most importantly, vices. Addictions make great ways of adding depth, in both a story sense and a gme sense. Sometimes vices come from the mind, fear of enclosed spaces could make it difficult for a character to navigate those sewers, and so on. they also come from the World. Racial profiling, or even plain outright discrimination can make even the simplest, most mundane tasks difficult.

Personal Details. Ah, this is the icing. A pocket watch they treasure, or a pair of goggles they seem to hang onto. Maybe a favorite type of weapon, or even a certain item that gives them a health boost. this are the little doodads that can give a character some real oomph. But overusing this is just as bad as overusing icing. Use it VERY sparingly.