TIFF (Tagged Image File Format): This
format originated with the Aldus Technologies Company which has since been
bought by Adobe. This format is used for high quality photographs and
is one of the few formats supported by PCs and Macs. Unfortunately,
it is large (i.e., usually uses no compression) and if it is compressed by
one viewer, another may not be able to read it.
GIF (Graphics Interchange Format): This format originated with CompuServe, can store 8-bits of information per pixel, and comes in only 256 colors. There are two versions: GIF87 and GIF89. The difference being GIF89 can support a transparent color. GIF files use the same patented compression algorithm as the UNIX compress program, and in 1995 UNISYS announced that it would collect royalties from anyone who used the patented technique. This prompted the release of the PNG (PNG's Not GIF format).
JPEG (Joint Photographic Experts Group): This format can store 24-bits per pixel and was created specifically for photographs. JPEGs make use of the fact that the human eye does not notice small color changes as much as small changes in brightness. It also is a "lossy" image because changes that the human eye cannot discern are filtered out of the image (i.e., data is lost). JPEGs offer four times as much compression as a GIF of the same image and can be compressed up to as much as 20 times. This means a 2 megabyte GIF would be a 10 kilobyte JPEG. JPEGs also display about 16 million colors as opposed to the GIF's 256.
Obtained from the book, The Internet for Dummies, 3rd Edition, IDG Books