Windows only: Freeware backup software FBackup includes special plugins for most popular applications—so you don't have to worry about which files to backup anymore, it's all handled for you.
FBackup can do all the things standard backup applications can do: automated backups, zip compression, password protection, an easy wizard, and even backing up open files—but the killer feature is support for plugins that tell the backup application exactly which files to backup—an extremely useful feature for easily backing up hard-to-find files like the profile folders for Google Chrome, Pidgin, or even Opera without resorting to manually finding each location from deep within a hidden folder somewhere. Sure, you can always backup the entire contents of your drive to make sure you captured everything, but even with today's hard drive sizes that's still a waste of space.
FBackup is a free download for Windows only. For more, check out your five favorite Windows backup tools, take a look at the five best file syncing tools, or learn how to automatically backup your hard drive.
The Online Tech Tips blog writes up how to migrate your TweetDeck settings from one PC to another, but the same principles should work for many applications based on the Adobe AIR platform.
Windows only: Downloadr is a small application that allows you to completely back up the photos from your Flickr account.
Windows/Mac/Linux: Looking for a quick way to upload and download files from a Google Docs account? If you're familiar with command line tools, check out GDataCopier. Once I installed a new version of 
