Hueswap is a web app for editing GIF color tables. Upload your favorite GIF, change the colors around, and then download the result! Try it out yourself at http://animalswithinanimals.com/hueswap/
Hueswap only works with real GIF files because it relies on the GIF's color table to work. It does not work with any fake pseudo-GIF formats like WEBP. (Fortunately there are free tools online for converting WEBP and similar formats into real GIFs.)
The way GIFs handle color info is fairly unique — it's called indexed color mode. This means that every GIF* contains an index (or list) of all the colors used in the image. This index is called a color table.
Hueswap hacks directly into a GIF's color table and lets you change the color values, leaving everything else unchanged. The arrangement of the pixels remains the same — only the colors change.
Hueswap was developed by José Garza and Benjamin Berg, based on a concept by Benjamin Berg.
* It is possible to create a GIF that has no color table (or more than one), but quite rare.