I like indie games. Independent developers can put more original games on the stores. They feel less preasure in shoulders than big company at development stage.
RPGs. They are really relaxing, as opposed to MOBAs or shooters. Just sitting down and grinding out a few quests never gets old and you never feel any pressure to perform (assuming you're playing single player).
something with a good story. It used to be RPGs, but lately I just don't have time for a 40+ hour game, so now ill take anything so long as it tells a good story.
I like MMORPG's the best. But I can't find any engaging ones on smartphone. But I have to admit that I don't really think the real Role-Play aspects can come to life on such small screens .. maybe tablets .. but still.
Otherwise for on the road or waiting I like those annoying small and pretty dull games like flappy bird and such, just because there is not so much time to spend on gaming anymore.