Here is an interesting link about Korean Air Flight 7, which was shot down by Soviet fighters in the 1983. It still hasn't been determined what exactly happened, but a number of conspiracy theories have appeared, such as:
The most interesting 'off course' theory is that the flight was part of a deliberate US intelligence gathering effort. The theories claiming KAL-007 did not crash relate to a number of issues. It is claimed to be unlikely that a single missile would knock a 747 out of the air, the loss of a single engine is not catastrophic for such a craft. Reports of the crash put the time from missile strike to sea impact at around twelve minutes, which is high for an uncontrolled descent. The crew aboard the airliner never announced a mayday despite there being two further communications from the 747. The amount of material recovered from the accident compares unfavourably with other crashes of roughly equal magnitude as does the type of material retrieved. That only two bodies were recovered, relatively intact, is also surprisingly low. All searches, either by the Soviets, Japanese or Americans were ended in early November, 1983.
The 'no crash' theorists do not go to explain why the plane was off-course, or why the Soviets would want to hold onto 260 or so airline passengers, except through the far-fetched claim that they were targeting a single passenger and felt it was necessary to keep all of the other people in captivity to conceal this.
I read another conspiracy a few months ago that the Soviets were testing a new system that day; the path of the plane took it near a major Soviet submarine base. Some feel that the pilots were on a CIA spy mission when it was shot down.