Mine certainly do! They adopt the most weird and wonderful positions, drooping over the edge of a shelf on a cat-tree, or right on the edge of the settee - from which they sometimes tumble over, and pick themselves up, looking most indignant!
They also like to lie with their heads on something hard - usually a book, as that is what is most often left lying around here.
I had one that used to drape herself across the top of the TV set, right on the edge (with her tail hanging down, bang in the middle of the screen). Her brother would sit behind her and gradually shift forward, millimetre by millimetre, nudging her imperceptibly... until the inevitable happened. She would roll off, with an indignant yowl, an acrobatic twist, and land with a glare and a hiss, swearing horribly up at her gleeful brother. They were half Siamese, and totally barmy - and I loved them to bits - never a dull moment with those two around!