During A-School we had some pretty good ones. Had a Marine who would take all of the popular songs and turn them into "Left, Right" cadence. Also, had a BUD/S drop out who sang their cadences. Some AE made up a few cadences on the go. Also remember running to Ke$ha's "Tik Tok".
During basic training, there is a set list of cadences you are allowed to march to, and you are only allowed to use them after you pass at least one drill exam. The running cadences during PT will all depend on your RDC.
http://army-cadence.com/Navy-Running-Cadence.php
From that list I remember: Man of Steel, Here We Go, My Dog Blue. I also remember Momma Momma, C-130, and They Say In The Navy.