I personally like to use TGA for when doing textures for games. Both Jedi Academy and the lith tech engine use the format (lithtech actually uses DTX but they are usually converted from TGA images). Unlike BMP, TGA saves an alpha channel and doesn't lose image quality like JPG does. I guess PNG is the same thing but I don't really see an avantage to use that format, AFAIK. Even though Jedi Academy can use PNG, PNG doesn't seem to want to load up in modview or md3view so TGA is preferred because of it. When it comes to just making images for web design, JPG is best when there is no need transparency. GIF is what I would use instead for images with transparency.
The cake is a lie... THE CAKE IS A LIE!!!!!