There are various ways of creating animated GIF images from video files under Linux, but most require cutting the video into images, then combining the images using GIMP or some other tools, but here's an easy way that only requires selecting the video, and optionally, changing the frame rate: Video 2 Gif.
Video 2 Gif is a python tool created by Lorenzo from atareao.es which uses Mplayer to convert the video to GIF and lets you configure the start and end frame, video size and the frame rate. It doesn't have many options, just the basics that allow you to create an animated GIF image from a video in seconds.
To see GIF created using Video2Gif from an YouTube video, click HERE (I've used 3 frames per second). The quality isn't great, but you can get better quality by using a higher frame rate (though this will increase the GIF file size). The GIF quality also depends a lot on the source video, so you'll get mixed results, depending on what video you use.
Before downloading and using Video 2 Gif, make sure you have mplayer installed:
sudo apt-get install mplayer
Then, download Video2Gif from here: English | Spanish
Once downloaded, extract the archive, double click "video2gif", select "Run" and you're ready to convert a video to GIF. The tool doesn't have a progress bar so once you click "OK", wait until Video 2 Gif closes!
Thanks to Lorenzo @ Atareao.es for Video 2 Gif!