All right I'll play. I hope all of these were Ninty published, think so anyway. Also kinda annoying 2010 isn't allowed haha, Sin & Punishment Star Successor would've been a high contender!
There's a lot of obvious greatest hits missing, like Mario Galaxy and Wind Waker but to my eternal shame I've not played enough of those to really speak on them.
1. Metroid Prime - played this years after release after remembering all the hype it got in magazines and thinking it could never live up to the 10/10 scores I was seeing. While I don't think it's perfect (that ending fetchquest...), it came very, very close.
2. Super Smash Bros. Melee - yeah its sequel had a better roster, but this one still gets pulled out from time to time. The leap from 64 to Melee is spectacular too.
3. F-Zero GX - I'm absolutely awful at this but it really, really hooked me for a while. If you could somehow capture its essence in pill format, rave culture would be revived overnight. *nyeeeeowwww*
4. Pokémon Gold/Silver - the Western releases were in 2000 & 2001 right, so I'm counting this. Improved on the original so much, people are praising the convenience improvements in Sun/Moon right now - Gold/Silver did a similar thing back then. And it was in colour! Had two main quests! A great sequel.
5. Fire Emblem: Path of Radiance - this felt very daunting initially. So many numbers & missions, anime tropes that were unfamiliar to me, it demanded slow methodical gameplay which I wasn't used to... But some of the characters really grew on me, I even read all those static dialogues it would let me. I messed up early on and tore a family of brothers apart. It tackled potent issues like racism head-on, a type of social commentary I often found lacking in games back then (also why I love Beyond Good & Evil so much).
6. Star Fox Adventures - yeah it's objectively not very good. It kinda falls apart halfway through and has some incredibly frustrating parts, a crap ending and some suuuuper cringey cutscenes. But that hub-world is gorgeous, the music is so atmospheric, I like the brief Arwing sections, the social order of the dinosaurs... But yeah. Rose tinted glasses all the way.
7. Wii Sports - feels kinda weird including this maybe, but EVERYONE wanted to play Wii tennis or boxing with you during this moment in time. Wii felt like it would revolutionize gaming, and I really wanted to buy into the motion illusion. It was so accessible, brought people together. For social impact alone this stands out.
8. Doshin The Giant - anyone remember this? The GameCube port of a 64DD game. My gaming has always been pretty limited to mostly Nintendo, but I did see god-sims like Black & White on PC at friends. To have something like that on console was pretty cool. I don't know if this would really hold up nowadays, it was pretty obtuse to be honest. But also very quirky and unlike anything else on the market.
9. Mario Power Tennis - sure, it's just tennis. But with singles, doubles, multiplayer, special moves, quite a big roster, a hilarious opening FMV, weird challenges and a few single player modes this was really cool. Secretly more fun than multiplayer staples like Mario Party.
10. Wave Race: Blue Storm - this GameCube launch title's controls were a little less intuitive than its predecessor's, but it was still a good time. The wave physics and just general look of the water really impressed me back then. Years later I read in a magazine how to unlock a "sarcastic announcer" who mocks your skills during the race. It feels like those types of dumb cheats have been less prevalent in recent years.
Boom! Maybe if I thought longer about it things like Eternal Darkness or DK Jungle Beat would push a few ones off the list but eh. Also makes me realise how little things I played on Wii... DKC:R was 2010 so that isn't eligible sadly.