Schnazuers prefer sharp cheddar or muenster to all other cheeses. Once in a while gouda (if I'm making reuben sandwiches). But the funny part is that my current schnauzer prefers her cheese shredded, not torn or cut in pieces, nor diced, or cubed.
Soft cheeses (ie not matured) because I can't have much of other cheeses. So mozzarella and philly are my cheese fix, apart from the occasional bit of cheddar.