It’s kinda too far back to remember the details, but I think I did a lot more of this back in the older days when hardware developments were much bigger steps and were basically essential. (And before laptops).
I’m sure I bought a whole new PC (386 or 486 or Pentium?) for Doom 2. (It would have been Doom 1, but by the time I’d saved up the money Doom 2 was already out).
I remember buying a CD Rom drive being a big deal, but the games I was upgrading for turned out to me mostly not worth it (FMV adventures).
But I think Bioforge and Discworld 2. Discworld 2 also needed a graphics card upgrade to get it running at the higher resolution.
I think a lot of them were iD games.
I’m sure Doom 2, Quake, Quake 2 and Doom 3 triggered upgrades, back in the days of 3DFX cards.
Half Life 2 may have as well, but I think it came out around the same time as Doom 3, and I think at the time Doom 3 seemed to be the big graphical leap.
Oh, and Jedi Knight: Dark Forces 2, but that was 1997 which was an amazing year for games and included Quake 2 as well.
More recently, I’ve been on laptops, and those aren’t upgradeable. So they tend to get replaced after a number of years, but not based on one particular game. Plus we had that long period of about 10 years where console hardware meant that we didn’t have to worry about upgrading or specs to play most games.