You can, I've done it several times to create forum avatars. The advantage of using GIMP/Photoshop for this is that you get way more control and probably better quality.
1. Record a short snippet of the video you want to turn into a gif. There is a wide selection of software available to do this, but I use
Debut (to record an area of my desktop, I.E the media player). Set the frame rate to something not too high. If you already have the video piece you want to turn into a GIF ready you can skip this step, ofcourse

2. Convert the video into a series of pictures, using
SUPER or some other program of your choice. NOTE: SUPER can convert a video into a GIF straight away but the result will usually be terrible color distortion.
3. Open the folder where the pictures are stored, select all and open them with GIMP. The pictures should arrange themselves in numeric order in the Layer window. The order in which they appear is the order in which they will be played.
4. Select "Filter > Animation > Play" to see a preview of what the GIF might look like. At this point you can edit the individual frames of the animation, trim down the number of frames (you want to use as few frames as you can get away with to save file size). If you want to, you can rename individual layers something like "Frame001 (300ms)" to specify exactly how long that frame will be shown. This isn't necessary if you want all frames to have the same delay, but it can be useful for optimizing the animation.
5. Hit "Image > Scale Image" to adjust the width and height as needed.
6. Save as .GIF. Select "Save as animation" and hit "Export". Apply whatever setting you want here; make sure you get the frame delay right (experimentation may be necessary). Anything less than 100ms is usually a waste of frames if you're doing a forum avatar. Again, you may have to experiment with the settings to achieve what you want.
Hope this helps. Some gif's I made this way:

