If Metroidvanias count, you all need to play Hollow Knight, it's absolutely fantastic.
Castlevania X86000 (Castlevania Chronicles on PS1) is my favourite Classicvania and possibly my favourite action-platformer ever besides Rocket Knight Adventures and Freedom Planet. It was also my first Catlevania. Weird place to start. The other 16-bit Classicvanias are good, too, but I prefer Bloodlines to Super because I'm a hipster like that. The first and third NES games are also good but I've never actually played Simon's Quest.
The NES Ninja Gaiden games are all a good time, too, and have aged surprisingly well (first played the original when I bought it on the 3DS eShop). The little known Master System NG is also pretty great.
There's this pair of freeware platformers by Locomalito called Curse of Issyos and Maldita Castilla (though this one has a commercial version) that are easily commercial quality, too. The former is an Ancient Greece themed action platformer in an NES style and the latter is a Ghouls 'n' Ghosts clone that I actually much prefer to its inspiration.
I'm surprised I haven't seen Cave Story mentioned yet, but maybe I just missed it.
The classic Sonic games are all still wonderful, in my opinion.
The first Mirror's Edge proved first person platforming could be done well though, weirdly enough, I feel like Titanfall 2 is actually the best first person platforming experience available now. Your mobility is obviously important in multiplayer but the campaign takes advantage of it in some really cool ways to create levels that are totally unlike any other modern shooter. It's obviously not a platforming game but I feel like it's worth mentioning because it gives you a similar rush.
The original Spyro trilogy holds up better than you'd think. As does Crash Bandicoot: Warped. The first Jak and Daxter and third Ratchet and Clank are also great. The first R&C has aged really poorly and I've never played the second. As for Jak, the second and third aren't quite platformers, imo. They have platforming segments.
