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.