GIMP is usually used to modify or create effects on still photos. However, it is possible to add plug-ins and extra features which let you do effects on short video-clips as well. For example:

1. I took a video clip (taken on a street nearby my house) to start with.
2. I more-or-less followed the tutorial "Gimp convert a video clip into frames " at​watch?v=p3vq2sqB30M
Basically, you start gimp in the directory you want all your frames to be extracted. In Gimp, you
a) click
video->split video into frames->mplayer based extraction.
b) select your clip, and the number of frames you want (I picked the default, which is 100), and prefix name for the numbers files (the default is "frame_")
now the frames will be extracted, and the audio will be placed in a separate wav file.
In Gimp (which you still have open),
a) Click
video->frames modify
b) Pick your filter. There are a lot of them. I selected cartoon. You can allow it to vary from frame to frame or be constant. I varied the effect from nothing in the beginning to larger radius and larger blackness level at the end.
It will over-write all the frames with the filter you selected.

Wait. Depending on the number of frames, the filter selected, and your computer, it can take minutes or hours. Do not quit Gimp when it finished!

video->master videoencoder.
This should put the modified frames and the old audio back. (It didn't for me - see below.)

Here's another example, but with a different filter:

System used:
ubuntu linux, with gimp 2.6 and all its bells and whistles, mplayer, and possibly imagemagick and other dependencies (I'm not sure).

Note: If video->master videoencoder does not work, you also need ffmpeg. Follow more-or-less​~gsteele/​ffmpeg/​ (use 30 fps, or maybe 25 fps for Europeans, but not 10 fps, as he has) to put the frames together into a video with no sound. This also requires all the frames be given sequential numerical names of the same string length (00001.jpg, ..., 00100.jpg, for example), which Gimp allows you to do. I did this since Gimp's videoencoder produced a corrupted avi file. To merge the video and audio, I "cheated" and used Final Cut on a mac.

You can also do this on a mac in FCP7, or FCPX using keyframes, but the effects are (artistically) more limited. The results are of higher quality and of course much easier to do (assuming you know FCP well enough).

Gimp has lots of cool effects, and with more flexibility, than FCP (at least the standard version, without commercial plugins). Also, Gimp is free:-)
This process creates serious pixelization, as you can see in the video. I actually experimented with some advanced options (skipped for simplicity in the above description) in other examples to select the highest quality possible. It made little difference. I actually think it was ffmpeg reassembling the frames into a video, and not Gimp, but I can't be sure.You can see the final frame

and compare that to the last frame in the video, which has more pixelization.