Let's have a grab from my note 4:
Anodyne, a surreal zelda type game
Terraria, if you like it on PC, why not on your phone?
Duet and the Impossible game, if you need to kill a few minutes and hate yourself (these games can be rage inducing)
Frozen Synapse, you can seamlessly switch between PC and phone, a great way to lock in a turn while on the bus
SpaceChem, a unique little puzzle game
Anything from Kairosoft, I love their addicting tycoon games, start with Game Dev Story
Kingdom Rush Origins, One of the best Tower defence games I've ever found
Ticket to ride, Galaxy Trucker, Monument Vally, 80 days, have been noted previously in this thread
Bounden, best to play this one with a loved one :3
A lot of games I pull from the humble mobile bundle, I love it that all the micro transactions are taken out and you get complete versions.