Prince of Persia: realistic animations with weight. also popularized a platformer subgenre, which was called cinematic platformer but unfortunately the life of the subgenre was cut short due to the advent of 3d.
Diablo: ARPG genre, and even more so loot rarity system (especially the four tiers common/rare/epic/legendary) and affixes in loot as well.
Half-Life: a lot of good things, sure, as pointed out by other comments, but I will also never forgive valve for popularizing the game not fucking starting for ages.
Rogue and maybe more so Nethack: roguelike mechanics.
some really obvious ones are Tetris: falling block puzzles and Sokoban: pushing block puzzles.
also now pretty much obsolete but Overwatch: loot boxes. they existed before, but Overwatch made them an industry standard.
i don't think they were as influential no. overwatch loot boxes were not only a monetization venue but also the main leveling system. whether you paid or not you always played toward a loot box. and couple with the game's massive success and popularity it opened the floodgates to this form of monetization to be a standard.