There are a plethora of a great fighting games out there.
Street Fighter, Mortal Kombat, Tekken all feel very different from each other.
I'm a big fan of Marvel vs Capcom, once you get into it, it's hard to play another fighter.
Then you have Smash Brothers, I never really liked the gameplay mechanics of Smash bros.
But there are some people who just love it. Its an interesting mish mash of Nintendo franchises.
One of my little known favorites is called Bloody Roar, your fighter actually goes through an anthropomorphic transformation.
[video=youtube;NyTqVq3TCHI]http://www.youtube.com/watch?v=NyTqVq3TCHI[/video]
The list goes on and on, Guilty Gear, Samurai Showdown, King of Fighters, Primal Rage, Killer Instinct (yea I'm that old)
It all depends on what type of fighting game you enjoy.
Theres some great anime fighters, Bleach Heat the Soul series on PSP, Naruto Ninja Storm on PS3, DBZ Budokai 3 on PS2.