Hard question... as I own most the games I like. But a few years back I went through a thing of buying PS1 classic games I couldn't own as a kid as I had no money then. So I have a lot of the games I really liked but never owned now. Only one I never got are the Discworld Series on PS1. They are not cheap.

Considering I never owned a Gamecube, and had to play through my uncle's, there's plenty of titles that come to mind. I'm currently replaying Wind Waker (HD on the WiiU), so I'm going to point out that one.

Kingdom Hearts and Halo 3

Definitely Undertale for me. I never actually played the game but i've watched a full walktrough of the game and I think I enjoyed it practically as much as if I was experiencing the adventure myself.
It's definitely a unique game for me. It's quite good for a one man creation I must say.

The Crash Bandicoot trilogy on PS1. I played those a lot (Mostly 1 and 3 though) at my friend's house, but I never actually got these games (Or a PlayStation, for that matter).

Really hoping the remake comes out on PC or Switch so I can finally own it =P

Paper Mario The Thousand-year Door for me. I rented that game like crazy when I was young and got all the way to the final boss, but couldn't beat it. I really want to buy it someday and finally play all the way through

starcraft on n64. i played it on pc alot... not sure if it counts but it is what comes to mind.

i dont know how good the controls would have been, but i was wanting this so bad and if i remember right it came out right at the end of the life cycle and the ps2 came out and i got distracted....

Uncharted 4, loved Uncharted as soon as I'd first seen a playthrough and more when I played it at a comic con both, but since I don't own a PS4 I couldn't get it :/
The good thing is that I finally could get my hands on a ps3 this year and blasted through the first 3,(in retrospect that makes me want to play uc4 even more)

Super Smash Bros. Brawl is one contender, as is pretty much any other game in the series. Tales of Symphonia, Chrono Trigger, A Link to the Past, Super Metroid, and a number of others could also fit. Really hard to pick just one when I haven't owned any Nintendo console after the NES myself, but I've played all of them a lot at my friends' houses.

I remember my brother and I wanting to get Gauntlet Dark Legacy for GCN back in the day, but it was a couple years probably after it's release, and it was kind of hard to find. My mom had ordered it online and we were looking forward to it until her purchase got refunded because they didn't have the game in stock.

I never ended up getting the game, and the PC version that released a year or two back wasn't that great, in my opinion. The closet I've found is an indie game called Hammerwatch, which completely nailed the Gauntlet vibe.