iOS/Mac/Windows: Free desktop application iPhone Explorer allows iOS users to export and backup data from their iOS applications without iTunes.
Sure iTunes can back up and restore some data on your iOS device, but it's not so great at backing up your third-party apps. Using previously mentioned iPhone Explorer, you can backup or copy apps (and their settings) to your computer or to another iOS device — and it can do all of that without a jailbreak. To backup system files or default applications, like iOS's built-in calendar, you'll have to jailbreak your iOS device. (Even if you're not interested in backing up apps, iPhone Explorer is still great for mounting your iOS device as a disk.)
Now more convient, you can simply backup or restore necessary third-party apps without hassling with a full backup and sync to iTunes. For more details on the app backup and restore process, see the How-To Geek's post.