I’m way behind when it comes to mobile games. I know I’m not a fan of the ‘on rails’, “swipe right to dodge”, and “up to jump over the chasm”, type of game.
I’m use to bottons. But I love action games… any with an easy learning curve?
What’s fun?
Obvious first question: iOS or Android?
Sorry.
Android.
I’m enjoying Farms and Castles. It seems quite simple initially. But it’s actually quite challenging. Like chess you have to learn to think several moves ahead.
(I’m also hooked on Alto’s Adventure, BUT you do jump chasms, so maybe not for you, but definitely worth a look. It’s a snowboarding thing, it’s kind of arty, lovely graphics, and remarkably calming to play!)
I’ve been playing Alto’s Advanture too much.
Horizon Chase is good, if you don’t mind paying a bit.
I love “arty graphics”!
I’m trying to thing of examples of games I would like. I can tell you I don’t like games like ‘Simpsons: Tapped Out’, ‘Protect your castle’. I would probably like a clever adventure game.
I liked ‘World of Goo’… but it’s not as good on my phone with my fat finger in the way.
I like games like ‘Toki Tori’/‘Lemmings’… but I don’t know if that helps because those aren’t mobile type games.
also liked a 3DS game called ‘Night Sky’… you’re a marble with simple obstacles to move forward… it’s very casual with ambient music.
I kind dig the motion controls for games like ‘Monkey Ball’, but ‘Monkey Ball’ doesn’t look like it’s that good of a game on the phone. Um… last night I found a cool game based on, (what’s the name of those wooden games where you’re tilting a marble’s platform through a labyrinth of holes again??)
Little help??
I like Alto’s Adventures. Thanks for the suggestion. 
No one?
I would heartily recommend a highly simplistic thing called Cirklar that in no way did I write myself.
iOS and Android.
Get the Amazon Underground store app:
You need to change a few minor settings to get it installed but they have a good number of normally pay games for free.
Monument Valley is a great one to start on.