Wombats - Moving to NY, awful song, but whenever it starts up I think it's Ash . . . I'm not sure which song, but I think maybe 'A Life Less Ordinary'? Also it sounds like Supergrass 'Caught By the Fuzz' as it ends (yes I have made it all the way through).
See also Kylie 'Wow Wow Wow' (or whatever it's called), when it starts I think it's that terrible 'Stars in their Eyes' by that Jack dude.
Other examples please.