Shaun Of The Dead

While not the first comedic zombie flick, it was the one that kicked modern zombie comedy into a whole other world!  Much, much better quality than, say, Night of the Comet!!  The very successful comic pairing of Simon Pegg (Shaun) and NIck Frost (Ed) caught the world's attention with the release of this.  They have since made Hot Fuzz (2007) and, most recently, Paul this year, which we will be viewing next.  If your thing is horror comedy, this is pretty much the apex.