In Michael Abrash's Graphics Programming Black Book, many chapters are dedicated to fast drawing of primitives, fills and copies using the 320x240 256-colour Mode X.
What MS-DOS games used Mode X?
There are many articles which refer indirectly to games using Mode X ('many games', 'popular games'), but I can't find any that name a game as using Mode X.
The only game that I've seen suggested is Doom, and that game doesn't use the resolution of Mode X (320x240), but the resolution of 13h (320x200) with some of the Mode X features, resulting in a mode referred to as 'Mode Y'.