It's a lot of work, but
App Backup & Restore for the apps and
Helium for the data or
Helium for both.
If all your contacts were entered as Google contacts, they're backed up on
Google Contacts, otherwise export them to a file.
Pictures, music, videos, etc., copy to your computer (or external SD card - or both.
The ROM? Not without a custom recovery (which doesn't mean that you have to root the phone).
Of course if you back up the ROM, you have everything else (except what's on the external SD card) backed up too.