The most often-used formats are files with the extensions *.TIF and *.EPS. The TIF format is a "lossless" format, meaning that all the information that was present in the original file is still available in the compressed TIF format—if it were opened up again, it would be an exact duplicate of the original file. TIFs are used for photographic images and are known as "raster" images.
EPS files, also known as "encapsulated post script", also called "vector" images, are a very different format that is defined through mathematical relationships--these files will look crisp and clear no matter how large or small you make them, and are generally preferred for the "drawn" type of image.
Click here for more information about the differences between raster and vector images.
Images in the *.JPG and *.GIF format are not generally acceptable for color reproduction unless they are converted correctly and have a large enough resolution, although they may occasionally be used in a black and white printing. They are usually quite small in actual dimension as well as in resolution. Both of these formats are "lossy" formats, meaning that the computer, in order to create these compressed image formats, throws out a certain amount of information that was in the original file. This information cannot be reclaimed even if you convert these formats to TIFs, which is why these formats are not be used in color reproduction by your professional printing house—the information needed for clean color separation is gone.
There is also some recent information that indicates that *.JPG files will gradually corrupt over time, making them a poor choice when it comes to storing these files for long periods.