I adore the Saturn, I own almost a full US library (damn you, Daytona NetLink) and have played through a lot of the games. Some great recommendations here, I'll add a few more that I feel are underrated or interesting.
DARK SAVIOR
Made by the Landstalker/Shining guys, this is an awesome action RPG with the novelty of battles going into a STREET FIGHTER-esque 3-round style before switching back to isometric for the core gameplay. The coolest thing about the game is that depending on how you play the first 15 minute sequence of the game, the course of the rest of the game is altered, so it essentially becomes 6 different RPGs, since each one follows its own branching story with different objectives, foes and locations. I usually never replay an RPG after it is done for the extra stuff, but these alternate stories are so damn charming I had to play through every one (and even discovered a 6th one that's never really talked about anywhere).
ASTAL
Beautiful game with large, layered sprite work and some heavenly music arrangements. The lead has a lot more moves in his arsenal than most platformer heroes, and the two player system adds a nice unique twist. Huge inventive bosses and a cutely rendered story, it's a tough game not to love. It was the first Saturn game I ever played, and at the time I was mad that I got it because I wanted a 3D game, but the irony is that of all the Saturn games this is one of them that looks the best today.
BUG!
The game I actually really wanted when SEGA sent me ASTAL as part of a 3-game Christmas promo was this game, with the cockier 'tude mascot in some 3D levels. It doesn't really maintain a good reputation today, but I've always really had an affinity for it. The dimensionality of the game with all the paths that go into every X, Y and Z axis is really cool and something no other platformers have ever really done before or since. There's some challenge too as the game progresses, and there is enough variety in enemies, level design and bonus worlds to make it interesting. For historians, this also marks Sonic's 32-bit debut (in the US, I guess, if you count his cameo as a rear-view mirror ornament in the Japan-only port of GALE RACER) since he's a guy you race in one of the bonus levels. Bug's one-liners are a bit too 90's today, but the other vocal mascots like Gex or Bubsy have that problem too. Not a great game, but a pretty interesting and unique one that I think deserves mention in the pantheon of Sega platformers.
POWERSLAVE/DUKE NUKEM 3D/QUAKE
I know you said no FPS, but I need to give a shout out to the boyz at Lobotomy Software who made one of the most kickass console first-person shooter engines of all time. The control and sense of speed in those games is perfect, and the light sourcing and 3D worlds are pulling more out of the Saturn than anyone ever would have expected. SEGA liked their work so much on POWERSLAVE that they got 'em to port DUKE and QUAKE with that engine, and they're really the best console versions of those games on any system (at the time) because of it. Really worth checking out on a technical level just to see what the Saturn could do when it was programmed right.
LAST BRONX
Another technical marvel, this is one of only a handful of high resolution games put out on the Saturn, and as a port of much more powerful Model 2 hardware, it's pretty amazing how close this game comes. VIRTUA FIGHTER 2 is another hires port that's always cited, but BRONX was brought home in a much more loving way with a bunch of extra modes and a lot of good unlockable content like unique anime endings for each character. As one of the first weapon-based fighters ever, it's amazing how SEGA nailed the gameplay right from the get-go, and the smooth frame rate and sharp visuals make it a delight to play. The Japanese version is the one to get with a second disc full of photo extras, but whatever version you get it's fighting game bliss.
MR. BONES
Weird-ass platformer that's a rare US-made exclusive. The game oozes personality, and there is so much variety to the gameplay styles - one level you're running left and right trying to collect your body parts, then the next level you're bouncing on a giant skull in a BREAKOUT kind of manor, and then in another you're doing an epic GUITAR HERO-like guitar solo trying to win over a crowd of possessed undead. Two discs of unbridled creativity and one of the coolest relics of the era, complete with some cool jazz FMVs.
Some other notable games I think are worthwhile too:
BURNING RANGERS: Sonic Team pushing the Saturn to the limit, a lot of great ideas, but kind of a dark empty game at times.
CONTRA: LEGACY OF WAR: They ported the series to 3D well, and this version has a 3D Glasses option which is a fun gimmick.
CONGO: THE LOST CITY OF ZINJ: Janky exclusive for the system, it's a fun DOOM-clone except with wild apes and spiders and shit.
FIGHTING VIPERS: Never gets any love next to VIRTUA FIGHTER but the caged matches and armor breaking system are really fun.
THE LEGEND OF OASIS: Top-down action RPG with a great 2D art style and solid gameplay, a prequel to the Genny's BEYOND OASIS.
DIE HARD ARCADE: One of the only 3D beat-em-ups we got in the US, but SEGA did the genre proud and ushered in quicktime events in the process. The gameplay and items you can beat people up with (apples!) is just over the top insane!
LOADED: Fun top-down action shooter for when you want to turn your brain off and just obliterate thousands of enemies to a badass techno soundtrack. Gets repetitive but serves its purpose before that.
Play some games and get back to us, would love to hear your thoughts!
