I'm looking to get an idea of how many databases are managed by a DBA these days. I'm not interested in the number of server instances, but the number of databases, and yes you can inlcude system databases (since you should be taking care of those, too.)
For Oracle admins, you can count the number of distinct tablespaces, or schemas, tied to your database instances. Those would be equivalent to a database for SQL Server admins, and for Sybase admins as well.