Note: DOSBox and ScummVM are not discussed here. For example, Might and Magic: World of Xeen is supported by latest ScummVM.

Some games have alternative engine(s) that support more platforms, features, options.

Some mods or data pack make games looks better, or provide better compatibility with newer OS.

Some cracks bypassed copy-protection, or fix bugs that original games never fix.

I know we already have quite a lot of those information, but they appear in different subforums and threads.

You may find some clues in:
GOGmix - GOG Linux games (without WINE and ScummVM)
GOGmix - Games that work on Linux natively

but there are more for sure..

Ah, this is a fun thread.
RCT Deluxe and RCT 2: OpenRCT2.
Theme Hospital: Corsixth.
Jazz Jackrabbit 1: OpenJazz
Jazz 2: Jazz2 (I thought there was a better known engine?)
Knights & Merchants: KaMRemake

Here's a list of Source Ports to get you started.

Morrowind: OpenMW
Tombraider 1-5: OpenTomb

OpenMW is fantastic. I have no experience with OpenTomb though.

https://en.wikipedia.org/wiki/List_of_game_engine_recreations
https://en.wikipedia.org/wiki/List_of_commercial_video_games_with_available_source_code
https://en.wikipedia.org/wiki/Unofficial_patch

Die By The Sword - https://www.moddb.com/mods/die-by-the-sword-xtended

I use it as the original version (which is what GOG provides) can be a hit and a miss at running without any graphical crazyness.

Might KeeperFX be a good example of what you're looking for?

CorsixTH might also be of interest.

Add UFO2 to openxcom its supported in the nightlies, infact the nightlies are the recommended way to play at this point. due to mod support with nightlies.

added

Thanks :)