I have very few games on my phone actually, but i got a few that have been on there for ages and will not disappear soon.
The first one is hill climb racing, its pretty much non stop grinding, but i like it, it still feels different every time!
Another one is Atomas, is about combining atoms and requires some thinking but not too much. The best part about it, is that it saves your progress if you quit during a game, so i often play this when i got a few spare minutes.
The last permanent game on my phone is Ruzzle, its a word based game and i just play this to keep in touch with the older members of my family that play the game aswell
Something new on my phone is pokemon go, i find it really funny to drive past places with multiple lures on it, and the see a group of teenagers sit there quietly looking at their phones ^^