I love projects like these. As someone who primarily plays old games having the ability to click an executable and it just run is a godsend. Some that haven't been mentioned so far ITT:
Augustus is a fork of another project called Julius for Caesar 3. Implements proper widescreen, along with rebalances the community has decided on, and the ability to zoom in, amongst other things. Still being worked on and updated to this day.
Flame is a patch to a decomp of Dungeon Keeper 2, one of my favorite games to play as a kid. Technically, DK2 works "fine" out of the box on modern PCs if you buy it on GOG, but there's still some little niggles that don't make it perfect, like no widescreen support, HUD scaling, etc. Flame fixes all that. It's fairly new, but I'm enjoying it so far.
The original Dungeon Keeper has a well-known sourceport called KeeperFX, so you don't have to run it in DOSbox or some other godawful implementation.
Multiverse Launcher is more of a client wrapper for Populous: The Beginning but makes it a much more enjoyable experience, and includes mod support as well.
syndwarsfx ports Syndicate Wars to PC, pretty barebones just gets the game running but it's another Bullfrog classic so that works for me.
CorsixTh is a port of Theme Hospital (I love Bullfrog games if you can't tell). Widescreen support, zooming, improved game logic, mod support and more.
Gardens of Kadesh is an SDL sourceport of Homeworld that incredibly enough, can be ran in your browser if you're so inclined. If you're a grognard like me and prefer playing the original and not the HD remaster this is the definitive way to play Homeworld. (Unfortunately doesn't work with Homeworld Cataclysm)
OpenXCOM is the best way of playing the original X-COM today, along with its expansion. Includes tons of mods as well, you do whatever the fuck you want with the basegame if you're so inclined. Really streamlines the process of playing one of the best strategy games ever made.
TRX is a sourceport for Tomb Raider 1, 2, and their expansion packs with development in the process of getting Tomb Raider 3 to work as well. IMO, this is the best way to play these games it includes mod support, controller support, and all sorts of other goodies.