Mel did NOT write the music for the theme
Despite the credit he is given here, Mel Brooks did NOT write the music for 'Hope for the Best, Expect the Worst.'
It is an old folk song, best known from the piano settings done by classical composer Johnannes Brahms. Here's one performance: http://www.youtube.com/watch?v=F0-vZ-zbOPY
(In case the link doesn't work, hunt for Hungarian Dance #4 for piano.)