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Common Digital Image Formats

JPEG stands for Joint Photographic Experts Group, the group that defines the standard. JPEG images are highly compressed (which means making a good-looking photograph with a small file size) but the compression is "lossy" (which means that every time a JPEG image is modified and saved, some information is lost).  Most image editing software lets you change the degree of JPEG compression; higher quality = less compression = less loss and a better image, but a larger file size.  JPEG is an excellent format to use for the web, but it's not a good format to save original images if repeated changes or modification will be made.

JPEG can also store "meta information" about an image, using a format called EXIF ("EXchangeable Image File Format").  Most digital cameras use JPEG as their primary image format, and they add a considerable amount of EXIF information to each image, such as date of photography, aperture, shutter speed and so forth.

Tagged Image File format, or TIFF is another full-color, non-lossy format intended primarily for storing original images.  TIFF is THE leading commercial and professional image standard. It is a flexible format with many options. This versatility can cause incompatibility, but nearly all image sofware will handle the standard TIFF types.  TIFF file sizes are large, so it's not suitable for use on the web. TIFF is the most universal and most widely supported format across all platforms, Mac, Windows, Unix.

Bitmap format, or BMP, is a format which retains all information. Unlike JPEG, Bitmap is not lossy, which means it's not compressed at all.  So BMP images are huge.  Therefore, it is not a good idea to put a BMP image on the web, or in a downloadable package. Bitmap is predominantly used in Microsoft Windows.

Graphics Interchange Format (GIF) is an "indexed" format.  This means that it uses a fixed list of colors (usually a fairly small number, like 256 or "8-bit color", or even less).  Indexed formats are very efficient for images with a small number of colors, like a simple logo; they're not suitable for images with a lot of colors, such as photographs.

GIF also offers two options most other formats don't have: simple animation and transparency by which a small animation can be embed on a web page and part of the image can be set transparent, respectively.  The transparency feature is good for putting logos on top of photographs.

Portable Network Graphics format, or PNG,  pronounced "ping", is a newer format.  It can operate in indexed mode or full-color mode, and their uses are different.

• Indexed PNG: this is a good replacement for GIF, which can be just as small, yet have more colors than GIF allows.  It allows full and partial transparency, like GIF.  But Windows Internet Explorer still doesn't support partial transparency in PNGs.
• Full color PNG: This is an excellent way of storing your original images locally.  Full color PNG does offer compression, but the compression is lossless, so you can make your images smaller without fear of losing any details in the image.  However, PNG compression is never as efficient as JPEG compression, so a full color PNG will be much larger than a JPEG of the same image.  In addition, it takes more CPU to read and write them.  Full color PNG is therefore not a good web format.
• Animated PNG: There's a format called MNG which is intended as a replacement for animated GIF, but without the limitations imposed by GIF (for instance, MNG animations can have full color depth and either partial or full transparency).  However, many browsers do not support MNG yet.

References

Wayne Fulton: Image File Formats - JPG, TIF, PNG, GIF. Which to use?        

Rick Matthew: Digital Image File Types Explained.