As for single database to multiple databases, a different database for each forum would be the way to go.
I disagree. phpBB has 29 tables in a "standard" installation. Suppose you have 10 boards, that's 290 tables. MySQL has limits on how many tables you can have open at a time, and it's not limited to actual application tables but includes temporary tables as well. You could conceivably run 50, 100, or more boards on a single server, each with their own database, but that's actually less
efficient, at least as far as I understand.
When a single database gets too big then it creates a bottle neck and can tend to choke a server. multiple databases will result in better performance, especially if you have a number of large active forums.
100 small databases is going to be less efficient than 1 large database, for reasons mentioned above.
Different users for each database would also be better for database performance.
If you do it right, with proper indexing and tweaking of the phpBB code, I submit that one large database is the way to go. Besides, there is no true "unlimited" databases, you're going to run into resource limits with lots of little databases much sooner than with one larger database.
Tuning efforts are different, to be sure.
Tuning a server for 100 small databases is different than tuning a server for one large database. But I submit that for the long haul it's better to have a single set of tables.