All Points Bulletin: Reloaded (APB: Reloaded for short) is your best bet by far when it comes to character creation. No joke, I could spend hours talking about the stuff I've seen people make in this game.
APB is an MMOTPS that takes place in the near future (I think. It's not like Si-Fi or anything) in a city named San Paro. A bunch of anarchists/criminals are tired of the government and start causing chaos in the city. To respond to this issue, the mayor essentially legalizes vigilantes/mercenaries to be the new police force for the city. In the game you get to pick if you want to be a Criminal or Enforcer, and you have to fight the other faction by doing missions and whatnot.
The amount of customizing you can do is insane. Not only do you create your character, but after that, you can create symbols that you can place on your clothes, cars, or as a picture to spray paint on billboards. You're able to place these symbols anywhere, so it's not like you can only put it in certain spots.
How things get customized:
Some of my own stuff (except for the first one):



As for other games (singleplayer ones) there's:
Fallout 3
Fallout New Vegas
The Saints Row series