The Doom engine is the game engine that powers the id Software games Doom and Doom II, as well as Raven Software's titles Heretic and Hexen, then finally wrapping its final commercial license with Rogue Entertainment's Strife. It is a sector-based engine, with 2D sprites representing objects, enemies and everything else that's not the map.
The best 3D game engine that connected the old technology with the new, and still withstands the test of time thanks to Carmack's wonderful open source advocacy.
Source-ports are still being used to create beautiful mods and indie-games, and it looks like they won't go away for years to come.
Easy of use: anyone can make a Doom-level and master the techniques with practice, even when using an advanced modern source-port. If you were to make your game using a Doom source-port (or something like Chocolate Doom if you prefer idTech 1 the classic way), it means that the action always feels good, and that the game runs smooth on pretty much all systems (even older systems).
The Doom community is still very active to this day, and is open to discussing any game that runs on idTech 1. Plenty of people are willing to help you out with the technical side of things as well, if you're looking to fork it off into your own project. Retro is a popular style these days, so why not build your retro-styled game around the best first person shooter engine ever created? You won't regret it.