EDITED Mar 5 2015
Updating ticket according to discussion in the comments.

• Make listDatabases command available to all authenticated users
• return the databases a user has read/write access to
• A user in possession of the listDatabases action type should as today be able to list all databases

======================
When running in authentication mode, show dbs will only work for a user authenticated on the admin database. However, it makes sense to list all of the available databases to anyone and request the authentication upon db selection.

This is currently not possible. The user needs to either know the DB name to connect to upfront, or connect as admin for show dbs to work. 3drepo.org has a use case for this.

This is related to:
SERVER-4823
SERVER-3181
(a list of names without info will be sufficient, as requested previously, although, in such a case the drivers would need to support querying for that)

MySQL and others will happily list dbs to any user.