A summary of responses by category!
The guy who just doesn't care (or wants to look cool): Because I can!
The philosopher: because the ability to step into the shoes of the opposite gender offers an experience otherwise missed.
The artist: By seeing the world through the eyes of another gender the story of the game can change in many ways, some drastic, others subtle.
The artiste: inflated due to ego, deleted due to length
The psychologist: It's interesting to see how player's actions change depending on the character they are playing. It also results in an interesting view on how closely the player connects with one character or another.
Oh, wait, MOMMY ISSUES!
The guy who does not want to be seen as gay: I don't want to stare at a guy's ass for 40 hours.
The guy: 'Cause I can see her (nekkid/in sexy clothes/scantly clad)!
The fanboy: 'Cause I wanna make a (insert female character name here.)
The Bioware player: Because the dialogue and plot actions (and in some cases available quests) change depending on your character's gender.
The WoW player: Because people treat you differently depending on your gender.
The G.I.R.L.: (Because its funny to see people's faces when they find out!)/(Because I like free stuff!)
The gamer: The stats are different.
Personally, when I play as a girl, I like to do it for the perspective thing, and because it actually does change the way I play.
And off topic: I think it might actually be interesting to see a game where the character's gender really didn't matter and wasn't shown, at least until the very end (I know that's been done with Metroid, but stick with me here...) AND, when the final reveal was done, the actions in game ultimately decide what the character looks like when it is revealed, including the gender. I think it would be interesting to see done, at least once, as well as interesting to see what people most often end up as (provided they don't use an FAQ).