I like a lot of "vintage" games that are a bit obscure.
1. Marvel Land, for Sega Genesis
This one is reminiscent of The Mario Bros. titles, but vastly more acid trip-py and colorful. The premise is the same in that your objective is a rescue a princess from an evil antagonist, but the levels are designed so beautifully and the whole game has a sort of theme park ride-type aesthetic. I adore it.
2. Goofy's Hysterical History Tour, for Sega Genesis
Despite the fact that it features Goofy, this game is actually pretty challenging if you can make it past the first couple of levels. It's a standard platformer in that there's a lot of precision jumping and inevitable falling to your death, but it's actually a lot of fun once you get the hang of all of Goofy's gadgets and when to use them.
3. Mortal Kombat Mythologies: Sub Zero, for N64 and PlayStation
I know everyone's heard of the Mortal Kombat titles, but this one was an OUTRAGEOUSLY difficult action/adventure platformer that followed Sub Zero as he attempts to steal an elemental map, and finally, to face Quan Chi. This game was the effectual bane of my existence for months, while I tried (and failed) to beat it. The smallest mistake ends in your death, essentially every misstep proves fatal, you're unable to progress past level 2 unless you play on Hard difficulty or higher, and the controls are the least intuitive I've seen in a game. Using an invincibility code only protects you from damage dealt by level enemies (not bosses, level traps, etc.) and is almost useless in the grand scope. I finally ended up beating it after binging on it for a length of time that I'll not mention, and the amount of relief I felt was... substantial. The game is pretty widely hated by both players as well as critics, but I actually thought it was a blast and still pick it up and play on occasion.
4. Fighting Vipers, for Sega Saturn
This is a Japanese import, and an all around great fighting game. It's fairly easy as far as the genre goes, but that doesn't make it any less enjoyable. The character designs are amazing, the levels are all interesting, and finishing moves have some interesting results depending on the level you're on. The final boss becomes a playable character after beating the game once through, and I can't forget to mention little miss Candy here:

There are many more, but these are some that have stood out to me.
