You should decide based on the type of image.
Jpgs are lossy. They lose information every time they are saved, but this helps make them smaller while representing complex images such as photographs.
If your image is photographic, choose a jpg to get the best-looking image at the smallest size.
Gifs, I'll trade for indexed PNGs. PNG has a better compression algorithm than gif. Like gifs, png's are lossless. They remember every bit of information in the image. Like jpg's, png's can have a bazillion colours (I think it's 16 billion).
Unlike either, png can do alpha transparency (though IE6 can't deal with it without help).
So any work that a gif would be considered for (logos, images with few colours), a png (with indexed colours to reduce filesize) should do that job.