I'm a big fan of PNGs, they're not lossy so if you don't use the alpha channel and use a single colour as a transparent colour, you don't get ugly colour bleeding like you can with jpg files.

The only downside being that they're not as small as jpg or gif files.

I remember the GIF patent issue a few years ago.. what happened in the end? Did it get resolved or did the "Burn Your GIFs" campaign persuade the patent holders that they were being stupid in trying to hold the entire internet to ransom.