Roleplaying groups are often like the A-Team, or maybe in some cases like a manufactured pop band. There's the clever character, the charismatic character, the mad one, and the tough one. Sometimes there's the sporty one or the sensitive one.
It's a matter of niche protection really. Everybody who plays wants a certain amount of "screentime", and the easiest way to get it is to fill a particular niche. The key to fun in games is often balancing the amount of time a particular character (and by extension their player) is influencing events. If a character gets too little screentime, the player feels hard done by. If one player character gets too much, then you have the opposite problem, everybody feels like they're in that player's shadow. Both states are frustrating.
Lots of games come with a way of making sure that everybody gets a chance to shine. Games with classes work well for balancing screentime. If you can easily tell a character's specialisation, then giving them screentime becomes easier. In D&D you can build lots of traps and locked rooms into dungeons so that a player with a thief gets lots to do. Of course classes also lead to problems when two players go for the same choice, they inevitably end up having to redefine their character to find a new niche. In general though, when your roleplaying environment is the Dungeon, and everybody has a clearly defined role, everybody can shine.
With more modern games, where players get free reign in character creation, it's actually more difficult to balance things. That free reign can give you a handful of character whose defining stats are practically identical, how's the GM supposed to guess when you want the spotlight? Ironically, the distaste of many modern games for min-maxing actually stops grabbing of niches. Such games will claim that min-maxing breaks "game balance", but what other balance is there than equal screentime? If you condemn your character to mediocrity, you'll never get that screentime. If everybody is anonymous the GM has to work harder to discover the thing that will force each character into the limelight. As if they didn't have enough to do anyway.
Fortunately many games come to the rescue with splats, broad archetypes like the Vampire clans, which can help define niches. Such constructs are no different to classes on a basic level, they give you an obvious place to start when thinking about the character, making it easier for the GM to work out when to give you the spotlight. Particular genres - modern action being a good example - thrive on such archetypes. That's why the A-Team is a good model for such circumstances, each character has a well defined role within the story. Thus every player gets an opportunity to be the one who's doing something cool.
However, if you conform too much to an archetype you end up having a cardboard cutout character, and if the game is trying to produce original and thought provoking stories, such characters can jar. The problem in this case is that the tools you are using to define your character's uniqueness don't work with the aim of the game. Using skills as unique points will only take you so far. I remember a game where one character was often referred to as "The investigation device", because that's all they were in game terms. They were only ever wheeled out when something needed investigating. The player had defined his niche, but not in a way that suited the game, and the character's screentime, and his enjoyment, suffered for it. What the character needed was personality.
When the story is the thing, the best way to define your niche is no longer through abilities, but through motivation and beliefs. The key is finding the drive behind the character, and making it shine through to the GM. Sure, anybody can have the same stats and skills as your character, but only your character is seeking the murderer of his dead brother. Motivators like this tell the GM when it is you want to have the limelight and what story you want to tell. Games like The Riddle of Steel, Sorcerer and my own Lost Gods actually give you tools to state, on the character sheet, what it is that will drag your character into centrestage. Even if no such system features are present then a well worded character concept can aid you here. Know what defines the characters attitude and desires. That way you can get that great scene where you confront your brother's murderer, and get that protagonising choice of how to deal with them.
So, depending on the game, how you define your niche will vary. The important thing is to think about it before the game, and make sure you communicate it to other players (especially the GM), so that players don't end up treading on each other's toes. Choose if you're going to be the strong one, the diplomatic one or the proud aloof guy driven by rage and advertise it. Just be careful that your character isn't the anonymous one, or your fun will suffer.