Does your cat dream or have nightmares?

[Randi]

When our Fister sleeps, we often see his paws, tail and whiskers moving - he is dreaming of course! But, he also has nightmares. When he sleeps betweeen us, he will sometimes suddenly jump high in the air like a rocket, with claws ready and make the most peculiar noises. He has obviously had a nightmare and looks SO confused - and he nearly gives us a heart attack! Sometimes when he sleeps under our bed, we can hear him banging his head against the bedframe. It often happens when he has been out in his old backyard after being inside for a couple of days.

Have any of you had similar experiences with your kitties?