Jazz Software is a freeware game developer which created numerous remakes or homages of various old school shooters within GameMaker. In contrast to most 3D games made with the tool, they are actually quite playable while also not outstaying their welcome. They were uploaded to the now defunct YoYo Games Showcase but are still accessible via the Wayback Machine. Other games remade include Doom and Rise of the Triad.
Wolfenstein: Operation - Iron Knight
The Nazis are attempting to build mecha, aka Iron Knights.
Link: http://sandbox.yoyogames.com/games/187051-wolfenstein-3d---iron-knight
Wolfenstein: Confrontation
Following their defeat in Europe, the Nazis have relocated to Imperial Japan.
Link: http://sandbox.yoyogames.com/games/188460-wolfenstein-3d---confrontation
Wolfenstein: Spear of Destiny
Inspired by the original Spear of Destiny, but features a level inspired by Spear Resurrection and finishes with a battle with Adolf Hitler without his mech suit. It uses sprites from the Macintosh version.
Link: http://sandbox.yoyogames.com/games/183860-wolfenstein-3d---spear-of-destiny
Wolfenstein: Return to Danger
Inspired by the original Return to Danger.
Link: http://sandbox.yoyogames.com/games/185436-wolfenstein-3d---return-to-danger
Wolfenstein: Evil Incarnate
Link: http://sandbox.yoyogames.com/games/189867-wolfenstein-3d---evil-incarnate
Wolfenstein: Ultimate Conquest
Link: http://sandbox.yoyogames.com/games/194219-wolfenstein-3d---ultimate-conquest
Wolfenstein: Rearmed
Link: http://sandbox.yoyogames.com/games/217534-wolfenstein-3d---rearmed
Wolfenstein: Machines of War
Link: http://sandbox.yoyogames.com/games/219124-wolfnestein-3d---machines-of-war
Castle Wolfenstein
Rather than a 3D shooter, this is a 2D shooting gallery game.
Link: http://sandbox.yoyogames.com/games/175919-castle-wolfenstein