We share a number of flu-type illnesses with pigs and ducks. That is often how flu epidemics begin, in environments where we, ducks and pigs live close enough together that we can have viruses jump species and evolve into forms that are rougher on all of us, like the recent bird flu epidemics. Human and bovine TB are close enough to cross-infect, HIV we can catch from apes and monkeys. Likewise bubonic plague and some kinds of typhus from rodents, Marburg disease and Lassa Fever from rats, mice, bats and possibly other animals.
I've even heard it suggested that there is a virus that humans share with a tree, the River Redgum (Eucalyptus camaldulensis), and that leprosy may originally have jumped species from amphibians. Don't know enough about the last two to really have an opinion, but interesting ideas.
