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 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.
Examples of what to use a GIF on.
JPG is the standard, use it for anything that does not have transparencies in it. A good thing to use JPG on is the typical basic sig... such as my current one,
PNG is a newer format, and allows for transparencies, but at much higher quality than GIF. Firefox supports it, and I would imagine IE7 supports PNG format as well.
Quick run down
Small file size for stills, animation, transparency
Pixelation, limited range of colors, lower quality for pictures
Widely used, good compression, range of quality
No animation, no transparency
High quality, good compression, transparency
Not as widely used, some support issues, no animation