This thread again?
I suppose being able to connect with your character is always important. but whether the character should resemble the player (age, race, gender, etc) is probably more to do with whether the emphasis of the game is storytelling or roleplaying. If it's a character-driven story-based game, then diversity in protagonists is surely only a good thing as it broadens the types of narratives we see (not just "Quick, Captain Squarejaw! Your girlfriend has been kidnapped!").
If it's a roleplaying game, where "player insertion" is more important, then yeah, I'd like to see a variety of possible avatars. At this point I suppose there's some other process that goes on inside the gamer's head - do they want to roleplay an aspirational "like me" character (white male, but Olympian physique) or do they want to play a completely different role where they can explore different social interactions, motivations and philosophies (different gender, race, moral alignment, different species even).
For what it's worth, I'm a white male and my current Gears 3 multiplayer caracter is Sam, a black female. I have no idea why. Variety, I guess?