Cats get chlamydia.
So do Koalas, and they're rife with it. It's actually a threat upon their population.
I don't know that there any any STDs, human or otherwise, that transcend species however.
HIV is suspected to have originated in non-human primates in Africa (so apes/monkeys), and transferred to humans, but whether that is through loveual means or not is unknown.
It's seems that SIV, the simian version of HIV, can transfer to humans who are involved with Bushmeat (meat gathered from non-domesticated animals, like chimps), and therefore it was passed on perhaps through the eating of/handling of infected simians.
After time it adapted to become HIV.
Or, alternatively, it's a possibly a result of unsafe medical practices.
It's probably not actually spread via loveual relations with animals.
