AGPL is used by a number of DBs such as MongoDB and Neo4j. I'm sure there are others, but these two are top of mind.
RethinkDB's drivers are Apache or MIT (I can't remember which).
Licensing the server as GPL/AGPL while making drivers Apache/MIT is an accepted practice in the database world as it provides the DB vendor with opportunities to protect revenue while the driver licenses protect developers from the GPL/AGPL.