Cooperative work (groupware) applications that provide a peer process near to each user.
Applications that need to present all users with identical state - shared whiteboard, shared view of a textual discussion
Less consistency: where a group of users are working on a shared document, but different users access different parts or perhaps one user locks part of the document and the others are shown the new version when it is ready.
Some services are effectively groups of peer processes to provide availability or fault tolerance. If they partition data then they don’t need to keep consistent at all. If they replicate then they do.