With me, sheets are king.

As mentioned, it's a very good litmus test in determining somebody's writing capability as well as how well they understand the setting, as well as making sure that their character is appropriate for the roleplay, be it their history, race, class, whatever. It also, as mentioned by other posters, ensures that there's consistency. I can't count how many times I've had to go back to reference my character sheet to make sure I kept facts straight. It doesn't matter how good your memory is, if it's an obscure thing you write in a single sentence six months ago chances are the details are foggy. 

By having a sheet, you also keep people from justifying having powers/ weapons/ connections or whatever that they failed to mention beforehand that makes the game rather unfair. I can't count how many times I've seen games where basically anyone who submitted a sheet was accepted that somebody would pull something in game that caused a rather lengthy argument, which does not bode well for a game's health. If you're a GM, asking for a good sheet is basically like asking for a resume. You want to find out if somebody's a good fit for your game, and it's one of the best ways to do it. If you just let anybody in the door, you have no idea what you're about to encounter or deal with. If you're lucky, it's somebody who understands what the game's about and doesn't exploit the lack of standards. But chances are, you'll have one or two people who will need to be dealt with, sooner or later.