I can't believe that no one is this thread has mentioned Tinkywinky. Now he has never officially been declared homosexual but there was much debate about him and homosexuality in childrens television back in the day. Also, even as a kid I could figure out that the purple dude with the handbag was supposed to represent homosexuality, and to show us that purple dudes with handbags are not evil or disgusting but regular people like us.
Now back in those days I was both old enough to put two and two together and old enough so that I couldn't stand the Teletubbies, but now that I think about it, this is actually a brilliant way to teach young children about homosexuality, as with all the other minorities the other teletubbies represented.
If the character is speaking and is influential to the story (an example would be Mass Effect) I pick a dude because I am a dude and will therefore have a much easier time putting myself in his shoes and relating to him in the story.
On the other hand, if the main character speak little or nothing all (example: Neverwinternights 2 or, more recently, Fable 3) and the only difference in the gender choice is whether I'll be looking at a dudes ass or a ladys ass the whole game, I choose a lady, for they have much prettier asses.