I don't play many games, but the few that I do play, I play a lot. As you can see, I've listed a couple of my favorites with links to guides I made on the left. (Note: I'm hosting a guide for Eternal Fighter Zero, which I didn't write, so if you have any questions about it email him.)
Party's Breaker (The Queen of Heart 2001) - The direct sequel to The Queen of Heart '99, this fighter focuses on 1 on 1 play featuring characters from the Leaf game Comic Party, which later became an anime. The same solid gameplay is present once again, but I mourn the loss of 2 on 2. The new Replay feature allows you to easily record matches into compact files that you can share with others.
Melty Blood - Melty Blood is a doujin (fan-made) fighting game based on the doujin game Tsukihime; it's a game made by amateurs (Watanabe Production) based on an original game made by amateurs (TYPE-MOON). Ironic, eh? The popularity of Tsukihime also led to the anime Shingetsutan Tsukihime that was released in 2003. Melty Blood has a lot of the features of Party's Breaker, solid gameplay, and cool characters. Revolve is currently working on an English patch. If you know anyone who can translate Japanese to English, send them on over!
Melty Blood Re•ACT - Melty Blood Re•ACT is an expansion to the doujin (fan-made) fighting game Melty Blood mentioned above, adding new characters and stages. The fighting engine is also tweaked for speed and many of the tactics from Melty Blood no longer apply. You need to have the original Melty Blood installed in order to use this game. Also, Watanabe Production created the professional game making group called French-Bread (FURANSUPAN).
Eternal Fighter Zero - Yet another "popular" doujin fighting game series. It became popular in Asia quickly because of it's VERY wide variety of fighting styles, import of almost every famous fighting game tactics, and, of course, famous characters from Moon, One, Kanon, and Air; however, it is also criticized for its too balanced movelists, unintelligent combo system, and lack of original moves. Another thing, you should be skilled enough because the gameplay is also hard.