A domesticated cross between a bobcat and a Yeti.
Mine is affectionate and mischievous (only two 'i's in that one, by the way), and much given to sleeping on his back. When there's too much light he'll throw one arm over his eyes. Yes, they are adorable. Stop me before I start posting pictures of the little beast.
They're big, by house cat standards: Fifteen pounds and up, more or less. They have very fine hair, like silk, fine enough to get in your eye and stay there for an hour or two before you notice. They also have tufts of hair at the tips of their ears and within their ears, and something very like a mane. They have very squared-off heads, with a much more imposing forehead than the average domesticated cat. They've got big feet too, like a puppy almost -- or maybe that's just mine.
In some places, if people see a cat carrier containing a large mound of gray silk with big circular eyes and ear tufts, they say "what the hell is that thing?"; but in New England they recognize it immediately. Around Cambridge at least, the common name seems to be "Coon Cat", "Maine" being left unsaid.
britishcoal: I've known few cats of any description who didn't do head-bumping, but the only Maine Coon I've known (mine) is certainly very interactive and affectionate. And adorable.