To add two additional points to @Zaralyndas detailed answer:
According to my own obervation as well as to this post on petguide.com (no affiliation), cats also show their comfort and happiness by stretching - here's a picture and an excerpt from the aforementioned post:
Licence: Creative Commons, Author: Watchduck, Link
Showing You Some Love
There are a lot of ways that your cat communicates her feelings with you. And as you get to know your pet better, you’ll be able to more easily decipher what she is trying to tell you through body language. Well, it turns out that your cat’s stretches might also serve as an indication that she cares about you.
Has your cat ever stretched out on her back in front of you, and perhaps even extended a paw towards you? That’s a sign that she is totally comfortable around you and she is even willing to expose her delicate belly to you because she trusts you that much. So, in addition to stretching out because it feels fabulous, this could also be your kitty’s way of letting you know that she really digs you.
A second observation I made was that one of my feline companions not just purrs when petted, he sometimes lays down completely flat with the stomach on the ground and extends his hind legs to the back and his front legs to the sides - we were joking that he's doing 'The Superman' move again. I don't know how common that 'move' is among cats, my other cat doesn't show this behaviour at all (she rather rolls around on the floor).