Oh yes, our cats not only have their blankies but pillows, sheets, chairs, couches, beds, tables...
They pretty much own everything but that is more than O.K. with me. In fact, I don't think I'd have it any other way. Compared to what they give me in return, it's the very least I can give them.
And, no, I don't have an out of control house; we co-exist just fine.