JPEG (Joint Photographic Experts Group): Files in this format have the extension .jpg. This is the format in which images from digital cameras are typically stored. It is a good format for continuous-tone images such as photographs. More detailed information about this format can be found here.
TIFF (Tagged Image File Format): Files in this format have the extension .tif. Like JPEG, this format is appropriate for continuous-tone images such as photographs. The difference is that TIFF files are much larger than JPEGs, because they do not discard any image information. TIFFs are used by professional printers and whenever very high image resolution is needed.
GIF (Graphic Image File): Files in this format have the extension .gif. The GIF format is useful for line drawings and sharp-edged graphics, and also for small looping animations that appear on websites. The color palette is very limited, and so this format is not suitable for photographs. Here and here are some sites with some great animated nature GIFs.
BMP (Bitmap): BMP file format deals with the Microsoft Windows Operating System (OS). BMP are usually uncompressed which causes them to be large files. In general, BMP files are accepted in a wide range of Windows programs due to their ease and simplicity.
PDF (Portable Document Format): PDF's, which are also known as Adobe Acrobat, is actually not a graphic file format. Though it can be used solely as a graphic file which can contain images, it was actually designed to contain and display entire pages which includes type and vector shapes as well as graphics and layout. For more info on this, and other types of graphic file formats, click here.