The only thing I've seen - and this was only while I was apartment-shopping earlier this year - was a property that disallowed rodents as pets, for the reason that if they get loose (and they always get loose) they could wreak havoc on the property. But I've had friends keep snakes and other terrarium-requiring critters at different properties with no issue.
Similarly, my policy was that if it was an animal that could make waste or otherwise cause damage to the carpet, it required a pet fee like a cat or dog would. If it had the potential to be dangerous (poisonous, aggressive, etc.) it was prohibited.