Basically every 3D FPS from the 90s -> mid 2000's allowed for custom skins & models, it's far less common now since games prefer character makers rather than letting people run wild.
<Erf> SkulFuk: gf just made a toilet sniffing joke at me
<Erf> i think
<Erf> i think i hate you
Trackmania²s games, a racing game community based, where you can customize your car's skin and even 3D model (but the hitbox will still be the same) (you can also customize your nametag a lot, with colors and stuff).