GfyCat is a new site (still in beta) that created more efficient versions of animated GIFs. You can upload your own video clips or grab sections from YouTube and convert them. The site uses HTML5 video to create smaller and faster versions of GIFs.
Here is an example GfyCat of Ted, my Cavoodle.
The process of creating a GfyCat is relatively easy. You can upload a video file (no longer than 15 seconds) or if your video is on YouTube or Vimeo just use the Fetch URL option. Paste in the URL to your video and enter the starting time of your grab and also the duration (again, up to 15 seconds). You don't need to login to create a grab, but if you do then your account will keep track of all your created GfyCats.
Once the process is done you'll be taken to your GfyCat page. The Links option gives you embed codes, and you can also choose to display the grab as a GIF. I had varying success viewing GfyCat files on mobile devices, so it's good that this option is available for compatibility. (GfyCat also has my favourite URL naming structure ever- with URLs like HorribleHappyBalloonFish).
Here's the finished product (if it's not displaying properly just tap on the frame and you'll be able to view as a standard animated GIF).