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.
In spite of drivers being non AGPL, companies with 'absolutely no AGPL' policy cannot try the open source version of these DBs which puts these products behind others. I don't think AGPL provides any real benefit for the vendor. Most small organizations will want their patches (if any) to be upstreamed so they don't have the maintenance burden. Most big organizations will want commercial support anyway. All AGPL does is discourage adoption.
There are plenty of non-AGPL DBs out there doing pretty well. Here are some examples of GPL/MIT/BSD style licensed DBs: Riak, Cassandra, Redis, MySQL, PostgreSQL, ArangoDB, CouchDB.
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.