There was a short piece on the Radio 4 Today programme this morning about earworms (with some annoying examples! - listen here for another week). Earworms are annoying snippets of songs that you can't get out of your head. The psychologist on the programme said that her department at Goldsmiths, University of London, was researching into the reasons they were so catchy (repeated hearing played a part, as did what state of mind you were in, and whether any of the words in the song caused particular memory associations; in addition, earworms often included long notes with intervals that are close together. The psychologist also said that it is believed that certain personality types are more susceptible to them than others).
The word 'earworm' is a direct translation of the German Ohrwurm. This definition of earworm is in the OED as its third definition. Earworm was in the earliest edition of the OED as another word for earwig. The first citation is dated 1598. The second definition of earworm (marked obsolete and rare) is "a counsellor who advises a monarch etc in secret".
Here is the website of the Earworm Project at Goldsmiths. You can report your own earworm experiences here.