Graphic Interchange Format (abbreviated as .GIF, pronounced with a hard G, so it's not Jif) was developed by CompuServe 1987. They're pretty universial, so they can be viewed from any computer. ONLY use .GIFs when you have flat colors (such as cartoons, logos, graphs and pie charts, and even text saved as an image). It's also 8-bit (256 colors), and will almost always take up less space, due to its compression.

The Joint Photographic Experts Group (abbreviated as .JPG, .JPE, and .JPEG, pronounced as Jay-peg) developed JPEG. .JPG has compression also, but its compression is lossy, and will suffer image quality every time you save. It won't degrade it that much if you save it once. But, if you continue and edit it constantly, you will see it. JPG has 16.7 million colors. JPG doesn't support transparency, but who cares, it's only for photographs or images with gradual color variations.

So, recap: Use .GIF for your website layout, cartoons, logos, graphs, pie charts, or anything with low colors. Use .JPEG for your photographs, game (the 21th century games) screenshots, and anything else with helluva different colors.

Never use .BMP for the internet.