There have also been long time problems between the CIA (which deploys spies overseas) and FBI (which goes after foreign spies in the U.S.). Early on, the FBI resented the CIA as the new kid on the block. There was also a culture clash because the CIA had a more Ivy League atmosphere, while the FBI saw themselves as "supercops" (although the key "special agents" of the FBI had long been required to be college graduates.) Most of the initial CIA leadership came from the World War II OSS, which heavily recruited Ivy League schools and Wall Street for the "best and the brightest" to lead the intelligence effort during the war.
Aside from all these problems, the big one is that the "Director of Central Intelligence" is the head of the CIA, but doesn't really direct all intelligence activities in the U.S. government, especially the increasing intelligence work done by various Department of Defense operations, the FBI, the State Department, the DEA and so on. The failure to prevent the September 11, 2001 attacks has put a spotlight on this problem, and no one has an easy solution. The most popular fix at the moment is to create a cabinet level post for the "Director of Intelligence" and give that position the power to order all intelligence operations to work together. This rarely works, and most people in Washington know it. But "something must be done," and creating a new bureaucracy is a favorite fix.
The U.S. spends nearly $40 billion a year on intelligence. This includes spy satellites, agents overseas and analysts at home. Since the late 1940s, when the CIA was established to coordinate all of the U.S.'s intelligence gathering activities, there has been a low level war going on between the CIA and the Department of Defense. This is because some 80 percent of the intelligence gathered and analyzed is used by the Department of Defense. This is an old problem. In the early 1960s, the Department of Defense created it's own "CIA" (the Defense Intelligence Agency, or DIA) to coordinate the efforts of it's own considerable intelligence gathering activities, and to handle relations with the CIA. But the Department of Defense increasingly saw the relationship with the CIA as one of the tail wagging the dog. As the main user of intelligence, the Department of Defense was increasingly feuding with the CIA over what to look for and how fast the stuff could be delivered to the troops that needed it. After the 1991 Gulf War, this resulted in scathing testimony before Congress by Army generals complaining that they got vital information from the CIA either too late, or never.