Man is a social animal - conspiracies happen all the time A "conspiracy theory" though, is usually pattern recognition turned up to 11 with judgement and discernment turned down to 1 Actual conspiracies like the FBI against Trump are way less sexy than what people invent
PRISM / ECHELON are examples of actual conspiracies that are entirely plausible - government bureaucratically gathers all communications that it can and partners with foreign entities to avoid directly violating the law because everyone involved is self-interested and risk averse