Picture of Jimmy Page's Guitar - on LZ's BBC Sessions?

Fonzie and Homer hit the nail on the head, Pawn. It's his infamous Danelectro - he used to pull it out at concerts for a special treat for audiences. I say "infamous" because the brand is generally regarded as a cheaper guitar (the clue here is the masonite and plywood body), but when Jimmy did a few modifications and then, of course, played it like nobody else could, you got a sound ultra distinctive. It's not really a good idea to pursue this brand as anything but a collector's piece; they just don't play that well or sound anything like what you would expect after hearing Mr. Page riff on one. Homer's link is very helpful for a "background" on these animals, and you can see how the company has upgraded so much on the guitar to make it a viable instrument.