The most obvious and most commonly used is the surrogate DBD testing. This is where the author of a module tests the connection to a database, through DBI and a DBD driver, to ensure that they can process queries.
I guess I'm somewhat guilty of this in the tests for DBIx::SQLEngine: I use the DBD::NullP driver (included with the DBI distribution) to perform some of my basic tests, but I also optionally connect to a user-specified database to create a table, run queries, and then drop it.
In my defense, the purpose of the module is to provide a compatibility layer that accommodates driver and database idiosyncrasies... and like Class::DBI, the module can't be fully tested unless you actually put rows in and out of the database.
That said, I've worried frequently about the proper way to notify people of this feature and allow them to select the DSN they'd like to use. I'll be reviewing the discussion here for ideas I can incorporate into my Makefile and t/*.t files.