This is still my favorite system. I think most of the really good games were mentioned already but I'll throw Silhoutte Mirage in there, though it is Japan only. I know there's a Playstation version released in the US by Working Designs, and I've read about changes they made and stuff but I haven't played it. Point is though, it's one of the best 2D action games I've played and I will always have fond memories of it.
I also really like Virtual On, and it was actually the main reason I originally got the system. Graphics and stuff not nearly as good as the arcade version (which I played years later) but it's still Virtual On.
Panzer Dragon games, Dragon Force, Astal, Fighter's Megamix, Albert Odyssey Gaiden, Shinning Wsdom. Shinobi
I'm glad someone else liked Astal. It isn't well known but it's a good game. Graphics, music, and gameplay were all very good but not much extra content (you can't even create a save file) so you prettymuch had to beat it in one sitting.
Sonic Jam is also a really good game, it's a collection of sonic1,2,3 & knuckles and has a cool 3D museum thingy.
Also for Nights, if you can find the Christmas Nights "demo" disk that is also really good and the data links with your main Nights file