iOS: If you like to annotate your tweets and messages with animated GIFs, we have a guide to make some of your own. But for those you didn't create, GIFwrapped is a handy tool to save GIFs in a vault to use later.
The free iOS app asks to connect with your Twitter account so that it can show you a stream of all the GIFs shared by people on your timeline, and with a couple of taps, you can share it in your GIFwrapped vault. Similarly, hook it up to your Dropbox and put any GIF in your GIFwrapped folder on Dropbox to get it on your iPhone. Finally, there's a handy search feature to look for any word and save the results (gathered from across the web).