A song, or an advertising jingle, that invades your consciousness and won't leave. There's no word for this in English, so here the Germans have the clear linguistic advantage (you can also "pre-pone" an event in German and officially "dis-invite" someone). Here's where German comes to the rescue, with Ohrwurm, literally "ear-worm." You can almost picture the cute little fellow camping out in your ear, singing the inane ditty over and over, cheerfully evading your increasingly desperate attempts to silence him.
I want hereby to start an official campaign to bring Ohrwurm into English. Shouldn't be too difficult. Just start telling your friends "Crap, that new Danii Minogue single is such an earworm." When they ask you what an earworm is, tell them, and urge them to start using it in their normal conversation. Note to entrepreneurs: trademark the word "Earworm" while it's hot! While on the subject, German has a word for a song that is popular for matter of weeks and then drops into the memory hole. It's an Eintagsfliege (One-day-fly), named for the sort of flies that live only a few hours (English: Mayflies; Latin -- pricelessly -- Ephemeroptera). One-day-fly doesn't really work in English, so let's just call these songs...Ephemeroptera. OK, perhaps not.