I have to declare I have not a been big watcher of documentaries - I generally (wrongly) think of them as being dull or too harrowing for me to enjoy so this will be a steep learning curve for me.
From what I have seen, documentaries, like fiction, also often have a basic three-act narrative: the set up (tease), the main action, the conclusion with an indication of how the characters have been changed.
Interesting examples of documentaries (from my limited experience) are:
Blackfish (2013) - this is definitely a "telling" documentary. It is the story of Tilikum, a bull orca in Sea World. It uses interviews of former employees and TV and film footage to enlighten us about the realities of animals kept in captivity for our entertainment. It also tackles corporate conspiracy. The film succeeds in making us feel desperately sad for Tilikum, whilst fearing him. There are some chilling moments that stay with the viewer for a long time. It achieved its goal of convincing me to join in the lobby against this treatment of orcas or other sea life. Lots of perspectives are presented but there is no real objectivity and it is the powerful subject matter which makes this work rather than anything innovative about the narrative.
Searching for Sugarman (2012) - I *think* this is an "asking" doc but there is a lot of controversy about this so I may have just been played! If it were true, the reveal in the narrative would be genius. Even if it is not entirely accurate, it makes for a very engaging drama. It does raise questions over how truthful documentary film makers should be. Some critics have called it "myth-making".
20,000 Days on Earth (2014) - an incredibly engaging biopic about Nick Cave. It feels like a movie but reveals a lot about how Cave works and collaborates.
Beware of Mr Baker (2012) - an excellent film about Ginger Baker which combines old footage with interviews and even brings in animation to illustrate the story. It is extremely well crafted, bringing in themes very cleverly and mixing a range of media approaches.
Pina (2011) - a brilliant film about Pina Bausch by Wim Wenders. We hear from her proteges and colleagues. Live footage of them sitting in front of the camera and moving but not speaking - that is delivered by voiceover. A very classy technique. Some surreal arty moments throughout make it fascinating and engaging. We get a strong sense of Pina's unique approach, unfettered creativity and her inclusiveness. I find dance to be mystifying and a rather 'up itself' but was still very inspired by this.