Dhewm 3 is a source port of the original Doom 3 (not Doom 3 BFG, for that you may want to try RBDoom3BFG). It's known to work on Windows, Linux, macOS, FreeBSD, OpenBSD and AROS, but it should work on (or be easily portable to) any system that supports OpenGL 1.4 with ARB shaders, SDL and OpenAL.
Compared to the original version of Doom 3, Dhewm 3 has many bugfixes, supports EAX-like sound effects on all operating systems and hardware (via OpenAL Softs EFX support), has much better support for widescreen resolutions and has 64bit support.
It only supports old Mods if they either don't require their own game DLL or have been ported to Dhewm 3 - see the Mods page for more information.
Mod-binaries who are supported, are bundled with Dhewm 3. External data is still required.
Note that while the Doom 3 source code has been released under GPL, you still need to legally own the game and provide Dhewm 3 the game data to play. See the How to Install section for more information.