Battleships is a game that's easy to play with just a pen and paper but if you want to make your naval battles a bit more exciting you could download BattleSea.
This free Android version is true to the time-honored guessing game. Your objective is to sink your enemy's entire fleet by tapping positions of the grid to discover where the boats are lying. If you score a hit, the piece of ship will explode and your phone will vibrate. If not, play passes to your opponent, who must try to guess where your ships are (BattleSea lets you choose the position of your fleet before the game starts).
BattleSea lets you play against the CPU or a human opponent. The computer AI is pretty good and you'll find that most of the matches are fairly close. Unfortunately, you can only play in multiplayer mode over a network, and it would've been nice to have an option to play against someone on the one device.
The graphics in BattleSea are neat and tidy, and the exploding sound and vibration effects make hitting your enemy all the more satisfying. I experienced few problems with touching the wrong square on the grid, but if you do make a mistake it doesn't matter because your target isn't attacked until you press 'Fire'.
Perhaps it's not the most dramatic and exciting war game you'll play, but BattleSea is a good reincarnation of a classic test of guesswork.