I think we can all get a pretty good understanding of the "types" of REAL secrets most Presidents knew about (during their terms) by looking back at the real history of these state secrets.There have been many laws passed since WWII making the classification process more open & setting limits on the length of time state secrets can be maintained as classified.
To show that most "State Secrets" turn out to be far less dangerous to U. S. security than their Hollywood counterparts, here is a quick list (off the top of my head) of "once classified" MAJOR State Secrets that has been made public, . There are many more, but this will help show that, while these are fascinating to look back on, they are not the stuff that would keep most President awake at night:
FDR- during WWII
1. We had broken the German & Japanese secret codes. ( Code named: Ultra & Purple respectively) So important it was really a "War Winning" secret!
2. We (the US) were engaged in a massive, nationwide program to build the Atomic Bomb (Code named: Manhattan Project)
3. That FDR (personally) had authorized the shooting down (assasination) of Japanese Combined Fleet Admiral Isoroko Yamamoto based on "Purple" intercepts. (this one event shortened the Pacific war & saved many thousands of American lives in WWII)
Dwight D. Eisenhower-during the cold war
1. That we were sending manned spy aircraft (Lockheed U2's) over both China & The Soviet Union ever since Kruschev had rejected Ike's "Open Skies" diplomatic effort to allow legal overflights by each side.
2. That there was no "Bomber Gap" or "missile Gap" that the American public feared so much. (revealed by the U2 flights)
John F. Kennedy- Early 1960's
1. That the Soviet Union had deployed nuclear capable bombers & missiles within Cuba. (led to the Cuban missile Crisis) While this was very dire indeed...It was so dire that it was made public almost immediately in order to deal with the threat.
Richard M. Nixon
1. That Howard Hughes mystery ship "Glomar Explorer" was not built to recover precious metals off the deep sea floor (as told in the "Cover Story") but was designed to raise an entire Soviet nuclear-tipped missile submarine from the deep pacific ocean floor.
These are historical facts &, while fascinating to look back on, I would guess that GW Bush &, now Barak Obama will not be losing much sleep over things the CIA knows & has told them. It's what the CIA doesn't know that will cause sleepless nights!
I'm a bit of a buff on this stuff & would love to hear any other additions that I missed.