Oh boy, another tough one. I definitely have a favorite documentarian: Ken Burns. But how to choose a favorite documentary from his body of work?
I'm gonna go with Jazz (2000). I really love The Civil War and Baseball too, and all three of those gave me a much deeper appreciation of different aspects of my country's history. The War was also quite cool, especially since I love learning about WWII. But of those four, I would rather watch Jazz again before the others. It gave me a new favorite musician -- Wynton Marsalis -- and helped me understand a lot of the music I would otherwise have shrugged off or ignored. Thanks to it, I own 4 of Marsalis' albums. This was pretty much an obvious fit for me, as the trumpet is a huge favorite of mine.
Yeah, I know this is supposed to be about my favorite documentary, not my favorite jazz musician, but I love how Ken Burns picks one really personable, knowledgeable person to sort of anchor his longer documentaries around, be it Shelby Foote in The Civil War or Buck O'Neil in Baseball or Wynton Marsalis in Jazz. In this case, it led me to develop a taste for Marsalis' music in particular, but the series as a whole is also quite awesome, even if you're not particularly interested in jazz music. I myself still prefer swing to jazz, but I like jazz a lot better than I used to now that I understand it a little better, and that's definitely thanks to this documentary.
Here's a very young Wynton Marsalis twenty years ago on Mr. Rogers' Neighborhood, just for the fun of it and cuz I watched this show all the time when I was little. I'd outgrown it by 1992, but it's still nice to go back and revisit the neighborhood now and then :-)