Mention has to go to Duke Nukem (I'm gonna go out on a limb here and say that quite a few modern 'badass' characters are trying to emulate him, with the witty one liners and overt masculinity being frequent give-aways).
After Duke it's gotta be the DOOM Marine or Serious Sam, for the sole reason of both having unholy body counts by the end of their respective games (I don't care what anyone says, you complete Serious Sam/DOOM on Serious/Nightmare difficulty, you FEEL badass).
Finally, Earthworm Jim. He's a worm, he has a big, red gun and he can kill enemies with his FACE (uses it as a skipping rope as well)...anyone who can deny his level of badassness probably took offense to him pulling a 'Kurt Cobain' if you left the controller idle for a minute or two.