I like sport games, Fifa 14 is a great one (I know 15 has been out already for some time). I also like casual or simple shooting games not too complicate just to distract myself for a few (or more) minutes. Examples shooting zombies, monsters, dog fighting planes, etc.
in general i really like FPS but it is PC gaming. on mobiles it is really hard to say - something that i can play for a moment and then come back to it - preferably rpg and puzzles
It depends a lot on my mood and on which device. Regarding mobile gaming I like runners and platformers like Rayman Jungle Run. In console gaming I play a lot of different genres: shooters (halo), racing games (forza horizon) and rpgs. Lately I like to play arpgs on my PC. Path of Exile is currently the only game I manage to play in my spare time every now and then.
As I get older and don't have as much time for games, I seem to be interested more in games where I feel like I'm making a difference that I can build on and lasts throughout, such as improving my character, altering the world, etc. So obviously rpgs, or shooters and strategy games that have rpg elements.
I recently played call of duty advanced warfare. This is one marvelous game that I loved the most. The graphics are just awesome, I cant distinguish whether this is a game or movie.