Supposedly the basic HP printer drivers got messed up in Leopard (I keep wanting to call it "Leonard"). It was reported a couple of days ago on MacFixIt. They say they it works intermittently but sometimes stops due to a perceived "broken connection" or the like. I was pretty sad with the HP drivers in Tiger, but at least they kind of work. Perhaps Apple does not want us to use HP printers? Go to HP's website and try downloading and installing the drivers for your printer and see if that helps.
I have an Epson printer and had the same problem after upgrading. I didn't need to reinstall the drivers, the Mac just couldn't see the printer. I just had to select the printer again and I was able to print right away.
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