The kind of conspiracies that happen all the time are tiny ones, and typically (and that's how the word is most often defined in text) about a small group planning to do something illegal.
The term "conspiracy theory" is instead used about when a (typically very large) group of people creates a conspiracy to suppress a scientific or factual truth, and that does not happen all the time - it's very hard to find even one case like that. So no, conspiracies, in this kind of context, does not happen all the time.