Any wads...

[KingofBabylon]

That has a different character that you play as other than Eternity Doom?

[40oz]

If you're referring to the status bar hud face, Biowar has a new "character" that you play as. The wad is pretty fun too.

[GreyGhost]

Chex Quest, Simpsons Doom, Toon Doom and Sonic Robo Blast 2 spring to mind.

[gggmork]

jar jar's last pineapple fritter

[KingofBabylon]

Alrightttt

[Phobus]

http://www.phobus.servegame.com/ph_virus.zip

ZDoom wad where youplay as something entirely different in an entirely different world.

Self-promotion aside, a lot of ZDoom weapon mods have you play as a different character - one that comes with new levels is Zen Dynamics - a widely acclaimed mod by Xaser. Batman Doom is a non-ZDoom wad that has you play as Batman (obviously).

There's loads out there though. It does depend if you want to go into source ports or not as to how many you'll get to, as a lot of the more adventurous ones are on ZDoom and its derivatives.

[KingofBabylon]

Yeah I already knew about Batman Doom, don't really like the looks of it though.

[Enjay]

http://doom.wikia.com/wiki/Chosen