Fox has announced that King of the Hill will conclude its run at the end of its 13th season.
It should be noted however that due to various delays (sports, etc.) and advanced production of animated programs, the show is currently airing episodes from only its 12th season.
Episodes from the 13th season won't even begin airing until April, so it's currently unclear when exactly Hill will finish up its run, but probably not until sometime during next TV season (2009-2010).
In other animated FOX TV show news, American Dad! has been renewed for a 5th season.