I don't play many mobile games. When I did it was almost definitely Candy Crush. I stopped playing once I found out that they just kept making levels and I could never actually beat the game. I also found it really annoying that to progress you had to: A) Either annoy your friends on FB with invites or pay for the levels, and B) That for some levels you almost had to use powerups (which you need to buy) to complete a level. It is more of a marketing/acquire the consumers money then it is a actual game.
Definitely Star Wars: Knights of the Old Republic. It feels almost feels a console experience. As for mobile exclusive games I'd go with Infinity Blade 3.
It's a nice robot/space game that only really takes time and not much strategy or skill to play. Other than a somewhat fast finger to line up cores. You get blue, red, green, yellow, and black robots you can mix and match to attack with by lining up 2+ same colored cores. My favorite style of gameplay was to get a leader with +1.5 or higher attack bonus for Blue Zetas and have a full team of blue + a friend blue leader that had + attack damage for either blue Zetas or all Zetas. Then I would proceed to wreck house with my blues, since blue is my favorite color. They've added new Zetas that are a little more humanoid too so you can get a busty girl with a few robot parts/wings. A couple of times I couldn't attack when I was unfortunate enough to not get any blues lined up but for the most part I do alright. Strategy only really starts to come in when it takes 10+ turns to kill the final boss of a stage. Then you need to choose when you want to use your ultimates, your ships ultimate (which you must remember you have, I didn't realize how to use it for so very very long) and if you can survive a hit you need to heal back as much as you can as fast as you can. That's when having something like a "convert x core to a heal core" Zeta Ultimate can be handy. Or something like "convert red cores to blue cores" Man I think I chained almost a whole screen together one time I was converting multiple types into blue and then just let it unleash. Wish I had the pressence of mind to screen cap it.
I actually played a lot of Hill Climb racing, it became quickly addictive. In general, I like playing puzzle games, a really good one is chess puzzle and I also enjoyed Unblock Me.