My version of this conspiracy theory is one that's neither terribly implausible nor hugely significant. But, when you are talking about the President of the United States, it's certainly interesting.
If you think of CIA less as the puppet-master of world history and more as merely one well-funded player in an international version of the municipal Favor Bank familiar from Bonfire of the Vanities and The Wire, then the idea that Obama got help from CIA-connected individuals along the way seems less shocking and more plausible. He's not the Manchurian Candidate, he's just a kid whose parents exploited Cold War tensions to get him a favor or two.
The key thing to recognize is that the President's parents were exactly the type of non-Communist leftists whom CIA constantly cultivated.
Barack Obama Sr. was a protege of the dynamic Tom Mboya, who was America's man in Kenya in the three way power struggle with Britain's man Jomo Kenyatta and Russia's man, Oginga Odinga. Mboya was publicly on the payroll of the AFL-CIO's anti-Communist outreach program and may have been on the CIA's payroll as well, according to David Horowitz's Ramparts magazine. Obama Sr. got to Hawaii on the American-funded Tom Mboya Airlift that brought young Kenyan elites to America for college. He later got his master's degree at Harvard, which was probably second only to Yale as a CIA recruiting ground during the New Frontier.
Although Obama Sr. criticized Mboya's non-radical and non-racist economics in his first published paper, he later worked for Mboya, as well as for an American oil company. Indeed, if Obama Sr.'s claims were true, he may have been the last man to speak to Mboya alive, and saw him gunned down in 1969 by a Kikuyu hitman likely affiliated with Kenyatta's cronies. Obama Sr. claimed to have been the only witness to have been able to identify the triggerman and that the Kikuyus tried to kill him for it. (Obama Jr. left all this out of Dreams from My Father, whether because the story was dangerous for his surviving Kenyan relatives 25 years later, because he didn't believe it, or because it violated his No Interesting Anecdotes policy in writing his book is unknown.)
Obama's mother worked at the American embassy in Jakarta, Indonesia in the mid to late 1960s, when it was CIA Central. Obama writes in Dreams from My Father:
She found herself a job right away teaching English to Indonesian businessmen at the American embassy, part of the U.S. foreign aid package to developing countries. ... The Americans were mostly older men, careerists in the State Department, the occasional economist or journalist who would mysteriously disappear for months at a time, their affiliation or function in the embassy never quite clear. [In other words, these International Men of Mystery were CIA] ...
These men knew the country, though, or parts of it anyway, the closets where the skeletons were buried. Over lunch or casual conversation they would share with her things she couldn’t learn in the published news reports. They explained how Sukarno had frayed badly the nerves of a U.S. government already obsessed with the march of communism through Indochina, what with his nationalist rhetoric and his politics of nonalignment-he was as bad as Lumumba or Nasser, only worse, given Indonesia’s strategic importance. Word was that the CIA had played a part in the coup, although nobody knew for sure.
Later, she worked for the Ford Foundation in Asia, which had a long history of ties with the CIA.
My theory is that at some point, the President's father and/or mother got in touch with old CIA contacts and asked them for help with their Hawaiian slacker son's advancement, such as getting him into the International Relations program at Columbia or getting him a decent-paying job at Business International. Obama would have been exactly the kind of second generation, suave, charismatic globalized individual with lots of foreign friends (including sons of Pakistan's political elite -- and this was in the early 1980s when Pakistan was the frontline in CIA's struggle against the Soviets in Afghanistan) whom CIA guys would have wanted to do favors for in return for favors down the road.
When I first started thinking about this, I said, "Boy, my parents sure didn't have any two-degrees of separation contacts to CIA!" But, then, I realized, actually they did, being old friends from Lockheed back to the 1940s with legendary engineer Henry Combs and his wife Jimmy. Combs was the "irascible genius" (according to Ben Rich's Skunk Works) who was the chief structural designer of the incredible SR-71 spy plane that went 2500 mph, and, before that, he played a major role in the U2 spy plane. These CIA projects were of world-historical importance in averting WWIII by reducing tensions by letting the U.S. know the Soviets weren't on the verge of attack.