Oh, 2D, huh? I got into video games later in life - missed the PS1 and all that, so the first (and only) fighting game I own is Soul Calibur III, though I did get blisters on my thumbs the week I got it; that must count for something, right? I have played Soul Calibur II (hence the purchase of the next one) and Super Smash Bros. Melee at what was ostensibly an anime club ("They're from Japan and they have shiny eyes! Now let's kill each other!").
That was a pretty awesome anime club, in retrospect.
I like the custom character stuff in Soul Calibur III though - it gives me an outlet for my addiction to character creation, but I don't have to mess with all that fiddly Sims junk.
My husband probably knows all sorts of cool 2D fighters - I'll have to ask him sometime.