This is a question that really evolves with me. Currently, the games that inspire me are: Dark souls, Destiny, and Super time force.
Each with their own ways of hitting certain notes for me. Dark souls as a gamer and developer is now a pillar of game design for me. It does everything so very right. I still haven't beaten the game but easily have over 200 hours in it on console and pc.
Destiny inspires me art wise. It is truly a beautiful world to look at, the environments, the sky boxes, the weapons and enemies. The art is top notch.
Super time force really inspired me pixel art wise and unique game play-wise. Genius concept with a pretty funny story to go with it. I like the effects of the pickups, its like a neon party going on when its crazy. Easily one of the most fun games I have ever played in my life.
Some shout outs to Zelda, Pokemon, MGS:2, Pax Imperia:Eminent Domain, Diablo 2, Phantom Crash and Dungeon Defenders. They have shaped the way I think about games significantly.