Do any document databases (noSQL) allow you to do cross database joins? I am currently looking at MongoDB and ArangoDB as the database for our web application, but neither appear to support cross-database joins, does anyone know if there is such a document database that supports this please?
You can do it postgres 

Update as of 9.3

You can now use the new postgres_fdw (foreign data wrapper) to connect to tables in any Postgres database - local or remote.

also you can use dblink functionality but it isn't part of the default PostgreSQL install, but you can add it in.-  dblink.