Catan for iOS ($4.99) and Android ($3.99) is an app-based version of the popular board game The Settlers of Catan. While the website (published by another firm) offers free play, the moderate cost for the mobile app affords one the ability to play offline against both AI players and against in-person human foes (or non-human foes, if you know any who are capable of playing). The app also allows one to play online against other players for free.
The basic app includes the standard Catan map plus a few others; for an extra charge ($9.99 for all expansions on the iOS app), all 23 variations become available for both local and online play.
While there are many free and worthwhile game apps, Catan is such a widely popular game that investigation of the app is worthwhile. If you enjoy Settlers, then Catan is definitely worth a look.
iPhone
iPad
See for Desktop Versions and other Versions Here