Android and iPhone - Battleships, or Sea Battle as they've now called it. (Don't forget their Tic Tac Toe Wargame also)
Tapatalk, so you're never far away from Subsim.
Android -
Tuner g-string (guitar tuner, stepson uses it lots).
Violin tuner (wife).
Metal detector (magic, but it works!).
Opera web browser.
Electro Droid (do anything with electrics whatsoever this is your app!).
Strava (cycling/running app, great for competing with random others).
Ebay/
Amazon.
Camera 360 - great for non-standard arty photos.
Chemistry Clock (tell the time in accordance to the periodic table e.g. 8:19 will read Oxygen Potassium).
What else do I use? Hotmail, Gmail, Google Search, Maps, weather apps, Lookout Security, TS3 Remote (see who's speaking on TS without an overlay on top of your game), Steam, spirit level, task killer, BBC iPlayer (TV, on your phone
).
I'm sure most is available for the iPhone too. I've not paid for any app so far after nearly three years of using an Android OS.