@Wiimeiser
Technically, GIFs can support any 24-bit RGB color, but there can only be 256 different ones in a given frame. So it ends up not being an issue if the image only has a few different colors in it. (Interestingly, according to Wikipedia, GIFs can have multiple image blocks that specify their own color palettes, so it actually is possible to have a GIF with more than 256 colors on it, but it’s kind of a hassle and results in quite large file sizes.)
They also only support full transparency. They can’t don’t have an actual alpha channel, so they can’t have partial transparency like PNGs do, meaning you can’t have antialiasing on transparent backgrounds.