Some Anglicans bang on about their "catholicity", and tie this into the episcopal succession (so they can look down on 'protestants' and stand shoulder-to-shoulder with Roman Catholics and Orthodox, even though those groups don't agree).
A lot of Roman Catholics object to the Roman bit.
All Nicene Creed believing Christians say they believe in the one holy catholic and apostolic church. Protestants tend to think of this as the invisible church, where those with catholic tendencies tend to think of it as the visible church.