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,
Examples
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.
Examples
Quick run down
GIF
Pros: Small file size for stills, animation, transparency
Cons: Pixelation, limited range of colors, lower quality for pictures
JPG
Pros: Widely used, good compression, range of quality
Cons: No animation, no transparency
PNG
Pros: High quality, good compression, transparency
Cons: Not as widely used, some support issues, no animation