GIF

GIF is old, proprietary but widely supported format. Today it's mostly surpassed by PNG - in all regards except one: support for simple animations. If you need animated icon or something like that - use GIF, by all means (all patents related to GIF are expired by now), but for anything else... there are PNG and JPEG.

There is a page on choosing image formats that will help you to understand the differences and how to know which format will be best for the intended use.

More info can be found on Wikipedia.