The BBC science page discusses how songs get stuck in your head . Scientists used songs like the Rolling Stone's "Satisfaction" (yeah, you're already humming it, aren't you) They then manipulated the tune, removing snippets (presumably representing my air-guitar solo), and played the song back to volunteers hooked up to an fMRI machine. They report in Nature that many volunteers reported the subjective experience of familiar songs continuing through the artificial gaps despite the actual audio silence.
In people who heard the song continuing, their the auditory cortex also kept its activity. The exact form of the activity depended on whether the tune had lyrics. In tunes with lyrics, the region with biggest differences was the associative (higher-processing) auditory cortex, presumably reflecting a meaning-based reconstruction of the song. In worldless tunes like the Pink Panther theme, differences in brain activity extended into primary auditory cortex (the area of cortex to which the main sound pathway from the ears first connects), as if the volunteers "hearing" the tune were reconstructing the sounds themselves.
The scientists' conclusions, consistent with other work, is that memories with a strong sensory component are associated with elevated activity in the brain region which handled the original experience. There's a lot more going on with a memory, though, than a strict rewind. I'm thinking about Proust's famous madeleine, which induced several novels' worth of non-taste reveries. That was some cookie! But also of traumatic memories , which may vividly incorporate the sight of something which was never there.
Meanwhile, check out this slang dictionary, WordSpy . I don't really like their etymology of earworm (I always think StarTrek, Wrath of Khan) but "Meanderthal" sounds tailor-made for Germans out on their Sunday walk.
The Beeb refers to songs' persistence as "brain itch," which sounds unpleasant.