If you are trying to update your iPhone or other iDevice, you may try to restore from a backup so that you do not have to recover your data. However, iTunes may ask for a password, one that you do not remember setting because you never checked the option for an encrypted backup. There are several passwords you can try to change the password, given that you can remember your iTunes Store password, etc.
Step 1) Try your iTunes Store password first. This is most commonly the password to restore your backup.
Step 2) Try your 4 digit unlock code for your device. If you have a more complex unlock code involving characters and such, try that too.
Step 3) Try 0000 as the password, sometimes the default password is in fact, 0000.
Step 4) Sometimes, the password can be a really old iTunes password that you set a long time ago but have since changed it. The original password is sometimes your backup password. This may be a bug in iTunes but try it and see if it works.
Step 5) If you are using a Mac, you can try using the Keychain method. First, open Applications > Utilities > Keychain Access.app. Second, in the search dialog, search for "iPhone Backup." Third, double click on the most recent entry for "iPhone Backup." Fourth, at the bottom of the dialogue box, click "Show password" and type in the administrative password for the computer. This will reveal your iTunes backup password!
Step 6) If you are using Windows, the only thing left to try will be to change your iTunes password on your actual account to access the iTunes Store. Then on the backup password dialogue, try the old password and the newly set password.
Step 7) Try your Windows Administrator password. This is a common solution. Also, even more common is to try the Windows administrator password that you used when you first set up your computer or when you first set up your iPhone.
Step 8) If you have managed to attempt all the steps and nothing has worked, it seems like you will have to restore and set up the phone as a new one.