Printers that cut paper too

I was printing out cover art for my DVD collection yesterday and thought, "Wouldn't it be great if my printer could cut the paper as it printed?" That would have saved me a bunch of trouble.

What if there was simply another ink cartridge embedded in the printer that could spit out a chemical that would dissolve any paper it comes in contact with? Or how about pairing a small low-power laser that could cut through the paper as the printer-head went back and forth along the paper?

You could conveivably make custom shapes in paper, meaning that you could easily print CD/DVD labels as well (without having to awkwardly stick printable DVDs/CDs into your printer), even complex cutouts.