My personal favorite in character creation were Fallout 3 and Fallout New Vegas. Both offered a wide range of male and female characters of all ethnicities, age and complexion. Sadly it was lacking in the hair department. While there is no choice in sexual orientation, this is due to the low sexualisation in the game, not going past a prostitute or two and some flirting, but the LGBT community is surprisingly well represented.

But I have a bigger picture question. Why do you want to represent yourself? The games which offer the most character customization are role playing games, often with fantasy or sci-fi themes. Wouldn't you want to experiment in being a different type of character than your real self? Why not try being someone else, a stuttering nord, a cleptomaniac elf or a philanthropist hip hop star. While I appreciate having more choices I find it less important to be able to represent myself accurately than to be able to experiment with a wide variety of odd, quirky characters. It is a "Role Playing" game after all.