If you were already depressed, Taxi's theme song would make you feel suicidal. But that's not really what the OP meant, I think.
Lost and Threshold had those horrible sound effects instead of theme songs.
Most children's shows have terrible theme songs. H.R. Pufnstuf had Jack Wild but, still.
And in the SF genre, merciful amnesia has blanked out most of the Greg Mullavey/Imogene Coca sitcom theme, the one with astronauts and cavemen.