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Re:PostgreSQL 9.2.4, 9.1.9, 9.0.13 and 8.4.17 released by selenamarie on Thursday April 04, 2013 @06:11PM (#5495605)
In one case, a large service provider is specifically providing that kind of database access to their customers.

And to be fair: http://www.shodanhq.com/search?q=mysql

Re:PostgreSQL 9.2.4, 9.1.9, 9.0.13 and 8.4.17 released by achillean on Thursday April 04, 2013 @07:31PM (#5495956)
You get a lot more results if you search for the service/ port directly! http://www.shodanhq.com/search?q=port%3A3306