The worst one I heard was coming up from SAN to LAX. We heard an Arrow talking to Palomar tower about severe engine trouble, attempting to make it in on the ILS (it was moderately low IMC that day). Fortunately he made it in.
Just a couple of weeks ago, a student pilot was on guard asking for help because he was losing his electrical system and already lost the radio display (obviously he it was still transmitting/receiving). I kid you not, twice some jackass said "You're on Guard!". That's what it's for dumbass!
I helped the guy get in touch with the approach controller in the area, as we both ignored the clueless guard cop. Can you believe that?