Separate applications, or services. I can t see any reason to use separate databases for a single app/service.
(note: replication, even multimaster, isn t a separate database. Neither is Sharding.)
I believe some on here are confusing Database with a Database Instance.
Example:
A phone book is a prime example of a Database.
Replication:
having 2 copies of the same phone book does not mean you have 2 databases. It means you have 2 copies of 1 database, and that you can hand 1 to someone else so you can both look up different things at the same time thereby accomplishing more work at once.
Sharding:
You could tear those phonebooks apart at the end of the white pages and the beginning of the yellow and hand them to 2 more people. You could further tear them at each letter and when you need susan summers ask the person with that section of the book to look for her.