The only two times I really went out to make myself in the world were Mass Effect and Fallout 3 (both of which I enjoyed doing so). For the most part, though, I make characters I want to play as.
Take Skyrim for instance. If I want to, I can make an honor-seeking Nord who enjoys picking fights, slaying dragons, and driving out those pesky elves. None of that describes me, but it is a character I like role playing in the world of Skyrim. However, I may decide I want to play a sneaky thief and/or murderer who gets a thrill from getting away with what she's not allowed to do. That's about as far from my personality as possible, but that was one of my favorite characters to play as in Skyrim. Being able to make the character look like how I see them can help a lot in making that role playing more enjoyable.
Take Skyrim for instance. If I want to, I can make an honor-seeking Nord who enjoys picking fights, slaying dragons, and driving out those pesky elves. None of that describes me, but it is a character I like role playing in the world of Skyrim. However, I may decide I want to play a sneaky thief and/or murderer who gets a thrill from getting away with what she's not allowed to do. That's about as far from my personality as possible, but that was one of my favorite characters to play as in Skyrim. Being able to make the character look like how I see them can help a lot in making that role playing more enjoyable.