For computer generated graphics (i.e. drawn by yourself in Photoshop, Gimp, etc.) JPG is out of the question, because it is lossy - i.e. you get random gray pixels. For static images, PNG is better in every way: more colors, scalable transparency (say, 10% transparent, .gif only supports 0% and 100%), but there is a problem that some versions of Internet Explorer don't do PNG transparency correctly, so you get flat non-transparent background that looks ugly. If you don't care about those IE users, go for PNG.
BTW, if you want animations, go for GIF.
