One of my favorite programs for iOS is DataDeposit (free on Cydia). It zips up a program's "Library" and "Documents" subfolders and uploads them to your Dropbox. This allows you to easily backup, restore, and transfer saved data between iOS devices.
The only issue is that it requires your device to be jailbroken. Something that goes outside of its own program folder (and outside of its sandbox) will never make it to Apple's App Store.
Well, there's a way to backup and restore data without having to be jailbroken.
First, you'll need iExplorer (free).
http://www.macroplant.com/iexplorer/
As of April 2012, iExplorer will sometimes give an error, saying you've reached the limit for open files on your device. The work around is to just open Preferences and hit OK.
List of programs and where they store their settings:
Games/apps for iPhone/iPod touch:
Amazing Breaker
/com.dekovir.AmazingBreaker/Documents/levelHS.xml
Notes:
The file is plain-text.
Angry Birds
/com.clickgamer.AngryBirds/Documents/highscores.lua
Angry Birds Rio
/com.rovio.angrybirdsrio/Documents/highscores.lua
Angry Birds Seasons
/com.rovio.AngryBirdsHalloween/Documents/highscores.lua
Angry Birds Space
/com.rovio.AngryBirdsSpace/Documents/highscores.lua
IM+
/com.shapeservices.implusfull/Documents/implus_accounts.plist
Notes:
No passwords are copied as they are stored in the system Keychain.
Infinity Blade
/com.chairentertainment.birthright/Documents/SwordSave.bin
Notes:
SwordSave.bin through SwordSave4.bin for slots 1-5.
If there is no SwordSave.bin file, game will start at beginning again, but you can select the save file you want after the intro.
iSSH
/com.yourcompany.iSSH/Library/Preferences/config.dat
iTeleport
/com.jugaari.teleport/Library/Preferences/com.jugaari.teleport.plist
Notes:
No passwords are copied as they are stored in the system Keychain.
SpeedTest
/com.ookla.speedtest/Documents/results.sqlite
Tapatalk
/com.quoord.Tapatalk/Library/Preferences/com.quoord.Tapatalk.plist
Notes:
No passwords are copied as they are stored in the system Keychain.
Where's My Water?
/com.disney.SwampyGame/Library/water.db