Games in which you can choose your characters appearance with a wide selection of faces, skins, clothes, etc. Also any games that feature the ability to change/alter weapons/armor (Either through using magical augmentations or, more desirable to me, a game in which you have a gun and can add different scopes, change ammunition types, add a grenade launcher, change the color of a gun, maybe even the barrel of the gun, or something along those lines).

Would greatly appreciate if PC games are mentioned.

*Morrowind and Oblivion, obviously.
*Hellgate: London is cool for weapon customisation.
*Hitman Blood Money has cool customisation for the weapons, but obviously you don't touch the character (except for disguise, Clown Massacre ftw). It's always hard to ditch your ballers' long slide when a silencer is needed :(
*Deus EX had some weapon customisation and was an awesome game
*most MMORPGs.

Custom Robo series
Armored Core series
Battletech and related
Urban Terror (mainly the funstuff for head combos)

I'm wondering if there are any free PC Armored Core-like projects running around the net that aren't horrible instance-based korean MMOs.