This.  SNES has held up amazingly well.  Link to the Past, Mario World, Lufia 2, etc.

On a related note, for me, N64 and ps1 have aged poorly.  Framerates are awful and everything is a blurry mess.  

Many adventure games on PC, like Leisure Suit Larry Laffer, Secret of Monkey Island, Maniac Mansion, Day of the Tentacle, King's Quest, Simon the Sorcerer...

Super Mario Bros. 3 is the NES game that aged the best by far. Super Mario Bros. 2 aged well too.

Commandos: Behind Enemy Lines + Beyond the Call of Duty

Heroes of Migh & Magic II

Your mom

This was my first thought. The gameplay is really timeless. Later releases in the series might have made the same experience better but I have not played them. It is a game just as fun to play today as it was back in the day. Simple but effective with fun characters and a very low bar to start playing while still being very difficult to master fully. 

SNES games have probably held up the best visually as 16 bit games just looks better than early 3D, but I think as overall experiences to me it's mostly PlayStation and PC games from the late 90s like Final Fantasy VII, Symphony of the Night, Half-Life, System Shock 2, etc.
And maybe Pokémon Gold and Silver thrown in there as well (at least in Japan they came out in the 20th century).

And Sam and Max Hit the Road. ^^

There are a few games I’d like to mention. No particular order. Also, by Japanese release dates, as many of these came out after January 1 2001 in most countries.

1. Xenogears for me. That game remains my favourite game in existence.
2. Super Mario Bros 3 may have graphical glitches, but it’s SO much fun. I prefer the shorter snappier and creative level design to other platformers. I also love the art style.
3. SimTower, SimCity, SimEarth, SimCity 2000 - I still really enjoy these games; and I love having SimEarth on in the background with parameters I set, and watching the world advance.
4. Donkey Kong Country trilogy - to me, this is peak 16-bit platforming design.
5. Sonic 1 and 2 - I love speeding through these games, while Sonic 1 is a little on the easy side, I still enjoy the crap out of it. Sonic 2 nailed the speedy levels and the difficulty combo.
6. Chrono Trigger SNES - my favourite version of one of my favourite RPGs of all time. Unfortunately, stuck on Wii for me, I hope Square does a pixel remaster of this. It’s noteworthy that this game was ported to the DS in 2008 at near full price and sold around 800,000.
7. FF4, 6, 7, and 8 are among my favourite RPGs of all time, and represent the Golden Age of the franchise. Each new Final Fantasy game felt cutting edge and advancing the genre. I’ll be playing all three of them this Spring, starting this week, all on Nintendo Switch. FF8’s once obscure game mechanics, like skill equipping (junctioning), crafting magic, items, cards, and weapons, are now common place in RPGs. I don’t think you can go wrong with any FF game, but the NES trilogy might be a bit primitive, although, I really enjoy FF1, but I’m wondering if it’s a bit too obscure for this list? I’ll soon be giving 2, 3, and 5 another chance, and maybe I’ll update this list!
8. Soul Blazer, Illusion of Time, and Terranigma - this trilogy of action adventure games is phenomenal, and I hope to see the ActRaiser treatment done in the future.
9. Suikoden 1 and 2 - I’m looking forward to playing these ones remastered on Switch. Among my favourite RPGs of all time, and still unique in their feeling.
10. Dragon Quest 3, 4, and 5 - although, I’ve only ever played the DS remake of 5, as they have yet to release the original Westside. Dragon Quest 1 and 2 are special to me too, but I understand they may be a bit primitive for most people… even in their time, as RPGs advanced VERY quickly in the 80s to early 90s.
11. Metroid 1 and Zelda 1 - Metroid, despite the repetitive design, this game remains one of the most intense gameplay experiences of all time. If you die, or are severely damaged, that is extreme punishment: you have to grind to get back to health. The only experience like it is the original Legend of Zelda, which is why I pair them. But Metroid 1 beats it, and any survival and horror game in terms of tension that will cause me to sweat at times. It, along with Zelda 1, are the two oldest open world games I’ve ever played - while primitive, the idea of having wide access to the world out of the gate and progressing by exploring that world, is a gameplay style I’ve loved ever since. Breath of the Wild is the first true successor to this concept—as right from Zelda 2 and Metroid 2, Nintendo abandoned the open world concept and shifted toward linear progression in those franchises. These aren’t for everyone, but they ages very well for me.
12. Link to the Past - this is the best paced of the linear progression games - I think Breath of the Wild finally nailed this as well after (IMO, Zelda games continuously failed miserably in pacing).
13. FF Tactics, Ogre Battle, Ogre Battle 64, and Tactics Ogre - this is mostly about the story, which is really well done in all these games, but all of them suffer from crazy difficulty spikes at time, and there are huge opportunities for you to run into a dead end because of a progression error you’ve been making for the past 10-15 hours. But if you’ve played them before, most certainly!
14. Fire Emblem 4: Genealogy of the Holy War - one of the best Fire Emblem games of all time, and the game that made me fall in love with the franchise, still not released officially Westside but was still quite big in niche fandoms in the 90s.
15. Earthbound/Mother 2 - while it’s a bit satirical on RPG mechanics and story stuff, it transcends this and comes into its own spirit. It also possesses some really creative and mechanics that are ahead of its time, and I play this one regularly. In fact, I broke a gaming fast (this year) with this game.

16. Kirby Superstar - Of all the Kirby games, this one felt most ahead of its time—from the DS/Wii era. This game (like  Chrono Trigger) was ported to DS in 2008 and sold for around full price and sold over 3 million additional copies.

I’m missing a bunch (no way I’m not). I really liked the arcade classics example above, for example. I don’t have the same attachment to those.

I’ll probably add to the list, later.

Mario 1-3 and Sonic 1-3.

Could name a ton of SNES game but going to mention a few more recent games instead. Breath of Fire 3, Tekken 3, and Castlevania Symphony of the Night on PS1, Soulcalibur on Dreamcast.