As long as you have well entrenched agencies like that there are going to be turf wars. Between Patriot Act and DHS (whose role is not just to "make the kids in the sand box play nice) that has been, for the most part, done away with. Also, its not like there are several agencies doing the exact same thing. FBI deals mainly with crimes that cross interstate lines and other federal crimes. CIA gathers intelligence, mainly humint, from remote locations around the world and NSA is our proverbial glass against the door listening in on people all over the world electronically. Sometimes their functions overlap a little and there's a turf battle but by and large they are apples and oranges.
The only way to stop all redundancy would be to merge all these agencies into one super-agency. The problem with that is that bueraucracy would strangle such an organization and nothing would get done.