For jpegs, gifs, and pngs, Webpurr will do it for you. If you'd like to make them on your local system, there are some apps that reportedly make them such as Acorn and Pixelmator for the Mac, ImageMagick and GIMP for Linux, RealWorld Paint for Windows, and PhotoLine for Mac and Windows. None of these products have been tested nor are is any recommendation implied by Webpurr, they are here for informational purposes only.
You can also upload short video clips (15 seconds or less) and they will be converted to WebP! We use ffmpeg on the backend, so most any mp4, mkv, webm, or avi will work. Videos must be a constant framerate of 30 fps or less. These limitations are in order to keep conversion times reasonable. If you would like to upload a videa that is longer, has a higher fps, or a variable fps, we suggest you convert it on your local system first. There are instructions on how to do this with ffmpeg and Google's libwebp tools below.
Unfortunately no known tools exist at this time. However, if you have Linux or a Mac, you can use a group of tools to do it in 3 steps. First is to convert the video to an image sequence, using ffmpeg (example: "ffmpeg -i input-video.mp4 -f image2 output%03d.png", the "%03d" will be replaced by a 3 digit numerical sequence). Second, use cwebp (or whatever image processor you prefer) to convert them all to WebP (might be easier to use a bash script to get all the images and send them to cwebp for processing). Third, use webpmux to join them all into an animated image. This will definitely be easiest with a bash script, as for every frame, you need to specify the image and the delay (example: "webpmux -frame output001.webp +250 -frame output002.webp +250 -frame output003.webp +250 -frame output004.webp +250" - the 250 is the delay in milliseconds - this example would give you a 1 second image at 4 fps). To convert fps to millisecond delay do: 1/<fps>*1000.
We have a subreddit set up, /r/webpurr, just for that purpose!