I'm probably going to list entries I've mentioned before in another thread, but here we go.
Ardy Lightfoot (SNES)
It's one of those games where the controls are lame and the difficulty occasionally ridiculous, but it compensates with charm in the visuals, some surprisingly good music, and... er, I guess that's it. Reminds me of SNES Lion King, although I think Lion King is slightly better. Anyway, it's a side-scrolling platformer where you play as Ardy Lightfoot, a meerkat guy with all the typical side-scroller moves. You can bounce on your tail like a pogo stick to reach high areas. Your buddy in this quest is Pec, a penguin (although he looks like a blue blob to me) who you can throw at enemies in a yo-yo fashion. Pec will go ahead and eat any enemies he touches. Later on you'll also find a powerup to turn Pec into a flying thing. If you hit an enemy, Pec disappears, but you'll find chests along the way to regain Pec. Get hit without Pec and you're done for. But you can still attack enemies by bouncing on them with your pogo tail. And a very useful tip I found out thanks to Nintendo Power: Hold Up for a couple seconds while standing still, and Ardy will pull out a screen thing to make himself invisible. Enemies can pass right by you if you have the screen up. Release to put the screen away, otherwise it goes away after a few seconds.
Chameleon Twist (N64)
Goofy little game that I think was early in the N64's lifespan. Probably was because the four characters you could play as looked nothing like chameleons. Some decent challenge and puzzles, cutesy perhaps. I tried playing one of the Gex games but couldn't get into it, and I never tried Glover, so this is the only low-budget 3D-platformer ripoff game I know of for N64.
Destruction Derby 64 (N64)
Don't know if this game's obscure, but come on, you win races by crashing into cars as hard as you can. How can that not be fun?
Lion King: Simba's Mighty Adventure (GBC)
This is the best Lion King game I've ever played. Granted this is next to SNES Lion King (I complain about its controls and frustrating difficulty), so that's not saying a lot. Looks and sounds a bit odd, yes. Music is either entertaining or gets on your nerves fast. The Timon and Pumbaa minigames are just as pointless as ever. But once you get used to the weird controls, it seems to control better than SNES Lion King (maybe it's just that there aren't as many cliffs to fall off of). The movie screenshots before and after each level are cool. And it even gets a little into Lion King II at the end.
On The Ball (SNES)
This was known in arcades or Japan or something as Camel Try. You have to get a ball through a maze. But the trick here is that you're rotating the maze itself, not the ball. The only control you have over the ball is making it speed up or jump. You'll also deal with pinball bumpers and gravitational pulling things and having to avoid X blocks... see, you have a certain time limit to finish each level. When you finish a level, the remaining time is carried over to the next plus like 20 seconds. If you hit an X block, 2 or maybe 5 seconds are taken away, giving you less time to get to the finish. Some levels may have gravity inverted so the ball falls up. Some levels might restrict how far you can move the maze so you'd have to bounce the ball along. Many challenging levels, amazing music, surreal pictures whenever you finish a group of levels... I recommend trying it out, this was one of my favorite SNES games.
Soul Blazer (SNES)
This is the first of a trilogy of RPG games. Soul Blazer, Illusion of Gaia, and Terranigma. I can see the influence of this game on Illusion of Gaia because you attacked enemies you saw on the screen (instead of having to go to a separate battle mode screen). But I never felt that Soul Blazer was an RPG, really. It was too arcade-like for that. What I got out of it was that you go to an area, annihilate every enemy you can find, then go back to town and advance to the next plot point. Then go back down to the enemy area and blast more enemies. I never got far in the game, I was still in the first town (if there were any towns after that). But it was still fun.
Super Tetris 3 (SNES)
Japan-only game, but it's almost completely comprehensible (maybe I got a translated version) and offers the best version of Tetris I've played (more so than The New Tetris). Addictive music (I love their version of Parorinka), some guy shouts out "Single!" "Double!" "Triple!" "TETRIS!" as you make lines, appealing visuals. I like how the background for a Tetris game changes as you go up in levels, so the sky is daytime at first and then eventually goes to night. Also comes with Magicaliss, which reminds me of Tetris 2 in that the blocks are different colors and grouped colors will disappear, and another version of Bombliss called Sparkliss (what we may know as Tetris Blast). Sparkliss has fantasy backgrounds. The first background of Contest Mode for Sparkliss has a couple slightly-animated dragons on either side of the well, thought that was neat.
I wonder what people thought of Hybrid Heaven and Winback: Covert Operations, both for N64. I never tried them, but people hyped up Hybrid Heaven like crazy.
Games I've heard of before that have already been posted in this thread:
Chip's Challenge (very fun)
Plok (played it LONG ago. Pretty much the only thing I remember is the music for the first stage, which is surprisingly good)
Skyblazer (meh, kind of fun)
Space Station: Silicon Valley (cool ideas, but too smart for me)
Tetris Blast and Super Bombliss (too bad I'm terrible at that game)
Uniracers (one of the best SNES games EVER - woo! By the way, the developer for Uniracers was who we now know as Rockstar North)