My controversial opinion is that candy crush is actually brilliant, yeah they want you to buy gold but it's more fun not to. The same goes for a lot of advert funded / in app purchase games - they're fantastic mobile games if you ignore the money option.

Morrowind ports and similar aren't great mobile games, they're great games but candy crush I can pull out my pocket when I'm waiting for a bus and get totally drawn into a few rounds. Airport control is another example, draw lines to direct landing planes and avoid a crash - super simple and repetitive but its complexity grows, cut the rope likewise is a true game in my definition because you learn skills and develop your personal ability beyond just learning game mechanics. They're engaging and enjoyable with a complexity ramp and nice easy to understand ui and graphics - they're everything a mobile game should be.

There are some great horror and story games too, especially the Indy ones