The first two songs that came to my head when reading this thread were Use Me and Michael by Franz Ferdinand.

Use Me is inappropriate when listening to and singing the song in public, as I randomly say "Use Me!" while listening to music on the train and gather odd looks from the people around me.
Then Michael has lyrics like "Michael you're the boy with the leather hips sticky hair sticky lips stubble on my sticky lips" which also attract odd looks when I sing along to it...