I wouldn't say these documentaries have "changed the world"; but they certainly had a larger-than-usual impact:<p><pre><code> "An Inconventient Truth"</code></pre>
<i>Wikipedia:</i> "Since the film's release, An Inconvenient Truth has been credited for raising international public awareness of global warming and reenergizing the environmental movement"
<<a href="https://en.wikipedia.org/wiki/An_Inconvenient_Truth" rel="nofollow">https://en.wikipedia.org/wiki/An_Inconvenient_Truth</a>><p><pre><code> "Killing for Love" aka "The Promise"</code></pre>
... about alleged murderer Jens Söring - <i>Wikipedia:</i> "Chuck Reid, one of the original investigators of the Haysom murders, has occasionally agreed to be interviewed about the case. His participation in the 2016 documentary The Promise led him to take his long-standing doubts about the outcome more seriously." Jens Söring returned to Germany two years later.
<<a href="https://en.wikipedia.org/wiki/Jens_S%C3%B6ring#Documentary" rel="nofollow">https://en.wikipedia.org/wiki/Jens_S%C3%B6ring#Documentary</a>><p>In general, I would say it's very hard to pinpoint real change to a particular movie, apart from bringing public attention to some issue. For documentaries which have done so, I suggest looking at movie awards, best of-lists (e.g. BFI) or the National Film Registry in the United States.
The Triumph of the Will comes to mind. Political propaganda films can be effective ways to change the world for the worse.<p>Many documentaries end up effecting permanent changes that may only be noticeable to people who live in a certain place or work in a certain industry. The Cove and Blackfish had a pretty direct effect on how SeaWorld treats its animals, but that doesn't quite rise to the level of "changing the world" as most would see it.
There are no films which "changed the world". One that really left (a negative) impression on me was Kissinger. Before this documentary felt like Lot in the storry of Sodoma and Gomorrha: there must be something good on this earth. After this documentary i changed my mind.
Loose Change recruited millions into the realm of conspiracies (Operation Northwoods, Mount Weather, etc) that had previously been pretty hard to find.