This app was mentioned in 6 comments, with an average of 2.50 upvotes
Small World also has a very good tablet version of the game (I think they are called Small World 2 because it's the second release of the tablet apps.. but it's the same as the Small World board game)
Android: https://play.google.com/store/apps/details?id=com.daysofwonder.smallworld2&hl=en
iOS: https://itunes.apple.com/us/app/small-world-2/id364165557?mt=8
Seems like the the games mentioned so far in this thread are for both Android and Apple.
Small World https://play.google.com/store/apps/details?id=com.daysofwonder.smallworld2
Blood Bowl https://play.google.com/store/apps/details?id=com.focushome.bloodbowlandroid
Sentinels of the Multiverse https://play.google.com/store/apps/details?id=com.handelabra.Sentinels
Galaxy Trucker https://play.google.com/store/apps/details?id=com.czechgames.galaxytrucker
Star Wars: Knights of the Old Republic
^ Astoundingly, this amazing classic is currently free!
for the on-android set, I would recommend Small World 2, and Ticket to Ride.
Both games are quite solid in the physical, as well as have good mobile ports.
Another one to maybe check out would be Splendor, as the physical game itself is really good, but I will admit to not having checked the port as of yet.
(edit to add links and Splendor)