Some of the games I currently have on my iOS devices:
(Most are free)
Happy Street
Pocket Planes
Tiny Tower
Pocket Frogs
Pixel People
I also still have and used to play these, but rarely do any more:
Japan Life
Trade Nations (to fill the void left after We Rule went extinct)
Tapped Out
Solitaire
Paint For Cats (not free, but affordable... and for my cats's entertainment)
Mostly I just play the first two, i.e. Happy Street, and Pocket Planes. Both are simple and work perfectly for spending two minutes at a time while waiting for something in the real life to happen (like idling moments, while cleaning etc).