Beyond Oasis is a fantastic Zelda-esque that is super cozy and really fun to play... if a bit surprisingly difficult.
Tinhead is super underplayed but so charming and original. It's really addictive to play and deserved more love.
Chakan: Forever Man has flaws for sure, but it's oozing style and cool factor. If you can overlook the sometimes wonky mechanics and blatantly unfinished latter half, it really is pretty great.
Dinosaurs for Hire is the best Contra-lite I think I've ever played and it's hilarious. There's so much charm to it and you get to play as dinosaurs... with guns.
Castle of Illusion and World of Illusion are just phenomenal Mickey Mouse platformers and super charming.
Ecco 1 & 2 are so atmospheric and beautiful, and the gameplay is really unique and addictive. It has problems, but it's so special in so many ways that I don't think that really matters.
Vectorman is incredible for its time and still really fun to play, if a bit frustrating.
Puggsy is one of the most unique platformers I've ever played and once you 'click' with it you'll be hooked. It does have a learning curve, though.
Comix Zone is straight-up one of the best games on the console. Just play it.
Castlevania Bloodlines is classic Castlevania to the core, but has a unique style to it and lets you play as a second character who's entirely a different playstyle.
Subterrania is a really cool shmup with a very unique exploration element to it. It's maddeningly difficult but it's just so cool and so captivating despite that.
Blades of Vengeance is an action platformer with strangely great feeling mechanics despite feeling budgety. The boss fights all have this weird way of feeling frustrating and cheap at first, only for it to 'click' and you realize how well designed they actually are.
Ristar is super underrated and a very unique take on the platformer genre. It takes a little getting use to but then you're just all in.
Pulseman is a GameFreak platformer that really deserves more love.
Kid Chameleon is a pretty interesting platformer with a transformation mechanic. You find different masks/heads that transform you into different characters with different abilities you use to traverse the levels. It can be kind of confusing, though.
Gunstar Heroes and Dynamite Heady are both fantastic run-n-guns that ooze charm and cannot be recommended enough. DH is particularly weird in a really fun way. Made by the same people.
Splatterhouse 2 is a grueling side-scrolling beat 'em up that pays homage to classic horror films. It's absolutely demented and really fun to play, though famously hard. Splatterhouse 3 is quite a bit different but pretty original and, despite some flaws, I actually think it's the better of the two games.
Earthworm Jim is a classic for a reason, and I definitely recommend it... but I always preferred B.O.B. There's so many little robotisms you can do to keep the gameplay fresh and the main character is just so likable. If you love tiny bits of fun details like unique animations that give the main character a lot of personality, you can't miss with B.O.B.
X-Men 2 Clone Wars is a really good action game where you can play as multiple different X-Men who all feel pretty different.
Aladdin. Totally different game from the SNES and just as good (arguably better.)
Zoop is a super unique puzzle game that my mom absolutely obsessed over. Do it, try Zoop for mommy! T.T Also Columns is an excellent puzzle game.
I could be at this for a long, long time but I think this is a good start. There's a lot to love on this console and I hope you find plenty to enjoy.