Capcom vs SNK 2 is the best 2D fighting game for the Playstation 2 in my opinion. It came out in 2001, approximately the same time it was released for the Dreamcast.
Capcom and SNK have teamed up to put many of the popular characters from their various fighting games into this game. Most of the characters from Street Fighter 2 and the King of Fighters series show up, as well as main characters from other series like Art of Fighting, Darkstalkers, and Rival Schools, amongst others. While the graphics are a bit dated, and pixelated on large screens, the control, music, and sounds are all great.
Where this game really excels, aside from the over 50 characters, is in the breadth of game modes and the excellent ratio system. In the main game mode you can choose between 1 and 3 characters to fight against enemy teams of between 1 and 3 members as well. However, if you only select one character, they get more life because you have fewer characters. This means that you're not forced to pick characters you're bad with, and you can mix up different characters and see how they perform against enemy teams. Aside from the main mode you can do a straight 1 on 1 mode, and survival modes as well, which force you to face an endless stream of enemies, trying to beat as many as possible with limited health.
Also, there are preset "grooves" which fundamentally change the way your character moves. For example, you can choose a groove that will allow you to block in the air, or you can choose a groove that will allow you to dash instead of run, or vice versa. You can customize the grooves and pick the abilities you like, and this can really add a lot especially when you're playing against others.
The game itself is a bit short, and the story is almost nonexistant, but it's a fighting game so you can't expect a great deal. A play through the single player mode will take about 10 minutes, but like all fighting games, there's tons of replayability.
I like this game a lot more than the Street Fighter Alpha series, and while the King of Fighters characters sometimes don't control as well as they do in the original KOF games, it's still the best 2D fighting game on the PS2. It's a little rare, so if you can find it, don't expect to get it as cheap as other used games. It's definitely worth getting though.