I have a Motorola droid with issues (but it still turns on) and I'm exchanging it for another. How can I move contacts, mail settings, etc. to the SD card so I can transfer them to the replacement phone?
Ideally I won't have to root it.
For contacts, the best way is to sync them to your GMail account. Settings->Accounts and sync Then when you add the same account on the new phone, it will sync them automatically.
For settings without root, I'm not sure.
If you are willing to root, Titanium backup is very good. It will save the settings onto the SD card. Then with the new phone, install the application and you should be able to restore the settings off the same SD card.
If you go in "Menu" -> "Settings" -> "Privacy" there is an option "Back up my data" that is provided by Google. I cannot say what data is backed up with this option but I guess email settings and device settings will be.
And as mentioned in another reply if you sync your phone with a Google account your contacts will be moved to the new device as soon as you log in.
Also if you have some applications that don't save to the cloud but you want to keep the data, there is usually an export functionality (check in the options menu of the applications) to keep the data into a file that you can import on the new device.
After doing all of this, last time I moved my content to a new phone, the only thing that I lost was the SMS history but I didn't really want to keep it anyway. I know there are some backup applications that support SMS history and don't need root access.