Hello there,
I use JPG's, GIF's, and BMP's on my computer. I have very specific reasons for using these three mostly. Here is some reasoning behind this choice.
BMP:
I use the BMP format when i have to have a 16 million color picture with no loss of image quality, usually when i know i'll probably have to modify it later. I dont upload BMP's however, because they are way too large. A picture stored in 24 bit color BMP format takes up a lot of room, and a 32 bit color BMP makes the biggest file you'll see so it's not good for uploading. If the BMP has 256 colors or less i convert it to GIF and store it that way.
GIF:
This format is especially useful for schematics and other line drawings. It makes for a small file size so it's very good to upload and store and since the image is lossless too you can edit it as many times as you want too without loosing image quality. It's only 256 bit normally, but that's good enough for every schematic i've ever seen as well as other technical documents like mechanical parts outlines.
A rather strange drawback with this format can occur if the software used to create the file, well, isnt all that good. Some programs like MSPaint uses a poor color translation algorithm that can render the picture all dotted up with the dots forming little patterns that distract from the picture. The solution is to use a better program, but a workaround is to make sure that the picture you want to save as .gif has only 256 colors or less. This trick usually keeps the picture clear of the 'chicken pox' audioguru was talking about.
JPG:
This format (used with an adequate compression setting) is good for real life still photos, like pictures of people and landscapes and just general photography where you use a digital camera or scanner to produce the image. It's a lossy format, meaning that the image quality suffers somewhat, but it usually doesnt matter when used with real life photo shots, and it makes the best color photo per byte of file space. It's only good for schematics when the schematic was taken with a camera or scanner, and not as good as GIF when the schematic was hand draw with straight lines on the computer using a line drawing program.
When to use each format? To choose the proper format you have to not only know the picture content, but where the picture originated (camera, scanner, drawn with a program, etc.).
BMP:
Only when you store it on your own computer and you need 16 million colors and you might have to alter it several times.
You can convert to GIF if there are 256 colors or less unless you have good enough software to convert more colors without introducing artifacts.
The GIF and JPG types require you to make a decision about the picture content and how it was produced. GIF is the best for schematics, but it's best when the schematic originated in a line drawing program and stored to GIF format. For some schematics taken with a digital camera it may be better to use JPG because of the way the shades of gray (or color) change throughout the picture. With the right software, you can convert a photo of a schematic to .gif and it will look nice, but in other cases you'll have to use JPG. If you're not sure you probably have to use JPG if it's a photo, but if it was drawn on the computer or downloaded as another format but it's still mostly lines and blocks then GIF is probably better. If any of the lines in the photo are not perfectly horizontal or vertical or diagonal then JPG may look better than GIF.
I should probably post some examples of when each format, GIF or JPG, is better because it's very hard to describe how this works.