There are a host of open source remakes of old game engines that fix bugs and update them for modern systems as well as add support for higher resolutions and widescreen aspect ratios. Here's a few off the top of my head:

• OpenMW for The Elder Scrolls III: Morrowind. This is probably the most famous one.
• Daggerfall Unity for The Elder Scrolls II: Daggerfall.
• OpenRA for Red Alert, Tiberian Dawn, Dune 2000, and (in pre-alpha form) Tiberian Sun and Red Alert 2 (the latter requiring extra fiddling with Github repositories).
• KeeperFX for Dungeon Keeper.
• OpenRCT2 for Roller Coaster Tycoon 2.
• OpenTTD for Transport Tycoon Deluxe.
• OpenJKDF2 for Dark Forces 2 and its standalone Mysteries of the Sith expansion.
• Arx Libertatis for Arx Fatalis, though IIRC the version sold now integrates an older build of it; one without the fixes for glyph drawing - it's worth upgrading for that alone as spellcasting is a nightmare without the fix.
• TRX for Tomb Raider I and II.
• Tfix, T2Fix, and the Sneaky Upgrade for Thief 1/2/3 respectively. These are mods, not wholesale engine replacements, but serve the same purpose.

These are just the ones I know of. There are probably loads more.

Edit: the Ur-Quan Masters for Star Control II. I can't believe I forgot about this! Star Control II is one of the best and most influential games that most people have never heard about.