Not my cat (he prefers boxes and baskets - he actually has a little basket that was once a bath set gift basket that he sleeps in), but my dog does! When I'm in my room studying or playing WoW, she'll give me a "look" and I know that look. I generally keep my pillows propped against the headboard (so I can have something soft against my back, of course) but when she gives me that look I know to move and place the pillows there so she can crawl there, lay her head on the pillow, and catch some Zz's.

I, also, toss and turn when I'm trying to sleep a lot. I know that if I want to keep my pillows I can't roll to the other side of the bed. My dog sees this as an invitation for her to take over my pillows.