Brothers and Sisters: The Dad dies to start it off.
Six Feet Under: The Dad dies to start it off. And then someone new dies at the beginning of every episode.
Desperate Housewives: The neighbor dies to start it off, and then becomes the narrator.
The Shield: An undercover Internal Affairs investigator is murdered in cold blood by the protagonist in the first episode, setting up the (a)moral context for the show.
Party of Five (?): I know the premise is the dead parents, but do they actually die to start the show?
Any others?
CSI doesn’t count in my mind. The death is that weeks mystery to be solved. You might as well count Homicide also then. Six Feet Under wouldn’t count either if it wasn’t for the father’s death at the beginning of the series.
CSI — dead person at the start of every episode.
What about The Fugitive? Didn’t that start off with a murder?
Lost – dead people all over the place.