TicTac5 is a board game that is very easy to learn yet difficult to master. You select a board of variable size (10x10 to 15x15 on iPad or 10x10 to 12x12 on iPhone) in which you must make an alignment of five of your pieces before your opponent does.
You can play against the computer (three levels) or another person by sharing the device. Note that the computer is very aggressive and will be even more so when it plays the first move.
This game is complete and free (but with banner ads), no in-app purchase or demo/full version.