I justgot a Motorola Droid X. I was looking for an app to record informal games for export in png for analysis later on my home computer. Shredder has an app that does an excellent job of this for under $10. You won’t be able to use it for most rated games, but it is handy for many other situations.
The Stockfish app in “play both” mode does well (on iPhone). The interface will save or email the game moves in pgn format.
Free.
Funny that you should mention that. I loaded Droidfish early yesterday and did just that. I like that it puts the pgn onto the clipboard at the touch of a “button” so that you can easily paste it into an email to yourself for when you get home to analyze. It’s free, of course. Used it last night and it was great–other than not winning the game. 
Having used Droidfish and Shredder for Droid, the Shredder program is better for the one purpose of casual game recording. The reason is that Shredder allows you to directly send the pgn via email without having to first save it to a file.
*On Droid
The Stockfish app for iPhone does the same (sends the pgn directly w/in email, no intermediate saving step).
Perhaps it is worth a try to ask the TD AND your opponent if you can use those apps in a rated game. If no one objects…
(Yes, yes…I know all the negative side effects–but it is worth a try)
I’ve done that and have gotten agreement.
It’s possible that I’ve missed it somewhere. To be continued.