Android: Previously-mentioned Carbon and Titanium are great tools for backing up your Android device, but they aren't free and require a rooted device for some of the best features. Easy App Toolbox fills the void as a free, powerful alternative.
The app allows you to back up your APKs to your PC, an SD card, or to cloud storage options like Dropbox, Google Drive, and Box.net (all of which are premium options in Carbon). A separate restore option built into the app lets you pull those apps onto any other device. This is especially handy if one of your favourite apps gets pulled from the Play Store.
The app is free and doesn't require rooting your device. You can back up three apps at a time for free, or unlock unlimited app uploads with a pay-what-you-want in-app purchase.