The number of colors in the image. Try to keep the number of colors in your image down to a power of 2. The less colors, the better. Large swatches of a few colors produce a much smaller file than an image with the same number of colors where the colors appear scattered amongst each other. This means that animated GIFs using, say captures from a camera source, will produce very large files.
Timing is important.
If you animate text, be sure you give your audience the time to read it. Animated GIFs can start playing before they are finished downloading. Many times it is good practice to make your first frame delay for a second or two. Making several animated GIFs that display synchronously is tedious frustrating work. If you are working on an animated GIF with a finite number of loops to play, remember that it will stop on the last frame.