Okay, in spending about 10 minutes looking around, I have already seen enough GIF format files to make me sick. More so because they don't need to be GIF.
To clarify, you should only use a GIF (Graphics Interchange Format) when you are doing an animation, or saving something that only has a few colors, not a range. For example, gif would work on an NES screen shot. GIF will suck on anything that has a gradient like effect in it.
Example of what to use a GIF on,
JPG/JPEG (Joint Photograpic Experts Group) is the standard, use it for anything that does not have transparencies in it. A good thing to use JPG/JPEG on is the typical basic signature or photo. In practise, printing house accept JPG/JPEG file from you; it just doesn’t have enough information in it to make the image look good.
Example of what to use a JPEG on,
PNG (Portable Network Graphics format) is a newer format, and allows for transparencies, but at much higher quality than GIF. Firefox supports it. IE doesn't supports!
Example of what to use a PNG on,
