For me, it's Super Smash Bros. Melee. I don't play this game anymore, but when I used to, it was a lot of fun. My favorite character was Kirby, because I liked being able to swallow my opponents and copy their abilities. Kirby also had great air skills, which is a plus. Captain Falcon was my favorite as well, because he had great speed and agility, and his falcon punch was quite powerful.
Dragon Ball Z: Budokai Tenkaichi 2 is also one of my favorite fighting games. I've seen a lot of people give this game negative reviews, but it actually wasn't that bad. It had cool graphical effects, the battle music were amazing, and the fights were really engaging and kept you on your toes. My favorite characters were Vegeta, Gotenks, Majin Buu, and Broly.