It really depends what I'm in the mood for. Examples time!
Hitman: Blood Money: This game makes me feel like a badass in the professional, efficient way. Nothing like going into a hotel, making some dead bodies, and walking out without anybody suspecting it was you - and the feeling of tension as you drag a body out of view just before the guard turns...
Bioshock 2: Ok, as far as being a big daddy goes, you're a pretty lightweight one - but once you get that drill charge attack, the feeling of being an unstoppable powerhouse surrounded by people who don't have a prayer returns quite strongly.
Batman: Arkham Asylum: I mean YOU'RE BATMAN. Surrounded by mooks, you just turn into this whirlwind of carnage. They can't land a hit on you, and you just flow through them, like an elemental force that leaves behind only shattered bones and concussion.