I'd say some of the survival games have made me enjoy the gaming on the mobile phone. I usually avoid those churning type games where you have to do a lot of things to go ahead. I think another fun element is that a lot of games that take input from your gesture, they tend to be more fun while playing the games. I love such games which add better experience in life.
I could remember when I first played halo, I couldn't believe there were short alien creatures and those short aliens are so sneaky. When I got to the part of visiting another planet on the ring, I was moved by the way they made the future look like.