Most of the good games for the system have been mentioned already, but I'll elaborate a bit and add a few.
Astal: A beautiful and innovative platformer. With co-op!
Clockwork Knight 1 & 2; Bug!; Bug Too!: Other Sega platformers, but they're not as good as Astal. Still worth picking up, though, as they're dirt-cheap and amusing for a couple of hours each.
NiGHTS: You fly around and collect stuff. Also an incredibly attractive game.
Panzer Dragoon games: The first two are rail shooters, and they're two of the best rail shooters ever made. The third is a free-form-flying RPG, but it also costs far too much money.
Dragon Force; Albert Odyssey; Shining Force 3; Shining the Holy Ark; Blazing Heroes/Mystaria: All excellent RPGs which are more than worth the money (except maybe SF3, which is also horribly expensive.)
Shinobi Legions: Perhaps the best Shinobi game ever made. At least, I like to think so. Awesome 2D ninja action.
Legend of Oasis: Sequel to Beyond Oasis for the Genesis. A cross between Zelda and a Final Fight/Streets of Rage-esque beat 'em up. Doesn't do much of anything different from the Genesis game, but it's still excellent for what it does.
Fighters Megamix: The best fighter available for the system. Go get it.
Saturn Bomberman: The best version of Bomberman available, but only worth it if you're willing to shell out $40+ for a 6-player multitap (not to mention extra for all of those controllers) in addition to the price of the game.
The Horde: An interesting, but flawed, action/strategy game. Worth playing if you're interested in something unusual.
You can also pretty easily mod a Saturn and play some good import games (The other two Shining Force 3 scenarios, Grandia, Princess Crown, and about 50 billion shmups.)
"'Casual games' are something the 'Game Industry' invented to explain away the Wii success instead of actually listening or looking at what Nintendo did. There is no 'casual strategy' from Nintendo. 'Accessible strategy', yes, but ‘casual gamers’ is just the 'Game Industry''s polite way of saying what they feel: 'retarded gamers'."
-Sean Malstrom
