Zoidberg wanted to mate with a female Decapodian named Edna. She thought he was gross and unworthy and after being seduced by Fry, she eventually mated with the Emperor and presumably died. Zoidberg also once lusted after a lobster from a restaurant and he's made out with a few weird space monsters. And also Professor Farnsworth.

He hasn't had any "relations" in the City which is probably for the benefit of us all.