Online GIF optimizer
You can also use: http://ezgif.com/optimize?url=http://link/to/image.gif
Lossy GIF compression
GIF compressor optimizes GIFs with Lossy GIF encoder, which implements lossy LZW compression.
It can reduce animated GIF file size by 30%—50% at a cost of some dithering/noise.
This tool shrinks GIF file size by reducing the number of colors in each frame.
Each GIF frame can use up to 256 unique colors, and by reducing this number, you can achieve a smaller file size.
It makes multiple variations of your input image, and you can choose the one that has the best size/quality ratio for your needs.
Remove every nth frame
The frame drop option can remove every second, third, or fourth frame to reduce frame rate and, therefore, file size. Useful for gifs with a high frame rate.
Another option is to remove only duplicate frames. This method will search for very similar, consecutive frames, remove them and merge their display duration.
This option keeps the first frame in the background, and makes unchanged parts of the following frames transparent.
The results heavily depends on the nature of the image. It may give huge file size reduction in some cases when images have large, static areas, e.g. recorded screen capture of some program, but most likely will give poor results for converted videos or photo slide shows, where every frame is completely different. The fuzz factor represents how similar colors can be considered as equal.