My cat is both obsessive compulsive and claustrophobic.
First, the claustrophobia:
When my daughter stays at my house, Oliver (the cat) like to follow her around a bit because she lets him into her bedroom. In fact, he likes hanging out in her bedroom so much that if she is in there and the door is closed, he will make a nuisance of himself until he gets entry - meow, rub up against the door, even climb up to the handle and attempt to open himself.
Once she opens the door and lets him in, he hunts around for a bit then settles on the bed first with his cat-like machinations and then settles into his own cuteness and just chills out. However, the minute my daughter closes the door and he's determined that he no longer has the ability to leave on his own, he makes an even louder racket demanding that the door be opened. It's funny as hell! He absolutely goes cat-shit nuts until the door is opened.
It seems that Oliver has "ritualistic" behaviors that might indicate OCD. For example, most times when I get home, he can hear me pulling into the garage so he sets himself up by the entry door. However,when I open the door, instead of greeting me there, he jets into the living room and sits himself on the first step where once he sees me, he first meows then rubs against the banister.
Last night he dis something oddly compulsive that was funny both for its compulsiveness and what it ended up looking like. He was laying on my daughter's bed and she was about to go to sleep. While I was laving some goodnight chatter with my kid, I reached for a paper shopping bag and for some odd reason, the sound of the bag frightened Oliver to the point where he felt compelled to run for cover. However, his OCD needed for him to touch every single thing between him and the door at least once as he left so while he was trying to rush out of the room to avoid this perceived danger (of the bag), he was slowed down by having to touch everything in his path (a sight that brought me and my daughter to fits of laughter).
Another funny behavior that I can't for the life of me figure out is my cat's thing for dish towels. If I leave a dish towel on the kitchen counter (heaven forbid), he will find his way to it, grab it as if it's prey and bring it to the "safety" of his food bowl. Hid food bowl is his turf, it's where he brings all his "kills" which aside from dish towels might be: pens, pencils, hair elastics (his favorite toy to play fetch with) and anything else he manages to come across.