When do you start thinking about eventual consistency for internal data?

Most of the time, for internal services, we shoot for strong consistency, especially with crucial info. But I'm starting to wonder if we're maybe going overboard sometimes. So, when do you guys actually start thinking about eventual consistency for your internal data stores or services? Are there certain kinds of internal data where eventual consistency is a totally obvious win, even if it means dealing with some inconsistencies later? Or do you just stick with strong consistency unless there's a super good reason to change?