Def Jam Fight For New York, The Takeover for the PSP is great fighting game. I did not have the chance to play it till just recently. I did however remember renting other Def Jam titles for my PS2 at the local video store a couple of years ago.
What I like about this game is that just pressing the buttons continually is not good enough to win fights(although at the very beginning you could, because the opponents you face and their level are not at all high). Timing each and every attack has some importance if you want to come out victorious without scratch. The graphics are excellent and the finishers make cool. Yea, the slow motion right before the last blow to the opponent is got to be the best feature of Def Jam.
The video above shows me playing. That is the third guy I fight. I am new to this game on the PSP, but have some time playing it on my PS2.