Most games are best left alone.

But some, by it's unique game design or atmosphere just cry for a remake, f.e.:
Bad Company 2 (2010)
Favourite game ever! Has tons of features and mechanics you won't find in modern Battlefield games. Destruction 2.0, "War Tapes" HD sound, dirty language & all the "legacy features" a Battlefield game used to have. Sadly with all the elite dev's leaving cancerous EA we won't get something even close again. Only cringe woke trash like BF2042.
Split/Second (2010)
One of the best arcade racers of all time. From Disney. You can trigger explosives and change the track, very Michael Bay'ish. Tried the multiplayer back then and it really sucked mostly thanks to no anticheat and loosers just triggering every explosive on you. So it added some extra challenge, lol.
Turok (1997) & Turok 2: Seeds of Evil (1998)
Turok introduced gamers to a world teeming with cunning enemies, traps, puzzles and deadly weapons all within a vast 3D environment ready to explore. Has a great soundtrack & atmosphere.
Stubbs the Zombie in Rebel Without a Pulse (2005) Be the Zombie. Kick A** and Take Brains
World in Conflict: Complete Edition (one of the best RTS ever made)
Gran Tursimo 1-4 (esp. for the classic tracks)
Metal Gear Solid Classics (Collection already confirmed)
Deus Ex
F.E.A.R.
007 Goldeneye
Super Mario (Classics incl. Mario Kart)
F-Zero
Blur
There is a remake on STEAM,
Arkanoid - Eternal Battle. Mixed reviews. Doesn't carry a lot of nostagia.
Grand Theft Auto 6's setting will be Miami, so you'll kinda get a remake of Vice City.