YouTube has quietly started rolling out their own GIF generator. It's not available for all channels yet, with only certain creators having the option available on some of their videos, found under the sharing options next to email.
The GIF generator is fairly straightfoward. When you select the GIF sharing option, you'll see a frame-by-frame of the video. Choose a section of up to six seconds in length to create your image. You can then add text to the top and/or bottom of the GIF you wish. Hit Create GIF and you'll have both direct and embed links, along with other sharing options, letting you show off your new creation wherever you please.