• Animal Icons: It Came From Japan - An Animal Planet special produced in the runup to Godzilla’s fiftieth anniversary in 2004.
• Bringing Godzilla Down to Size - A documentary on the genre’s origins and legacy, originally included on the Rodan / The War of the Gargantuas Classic Media DVD set.
• Godzilla & Hiroshima: The Dawn of the Kaiju Eiga - A documentary that explores Godzilla’s nuclear origin, and the influence of the nuclear scare on the genre.
• Godzilla 1954: The DVD Shelf Movie Reviews - A run-of-the-mill but informative YouTube documentary on the making of the original Godzilla.
• Godzilla 60th Anniversary: The Amazing World of Japanese Special Effects - A 2014 NHK documentary looking at the sixty year legacy of Godzilla and the history of tokusatsu.
• Godzilla and Other Movie Monsters - A documentary feature that explores the history of monsters in storytelling, from the earliest dragon legends to Japanese monster movies.
• Godzilla, King of the Monsters - A documentary produced by the BBC in 1998 during the runup to the first American Godzilla film.
• Hail to the King: 60 Years of Destruction - An independent, crowd-funded documentary by über-fan Kyle Yount (kaijucast) that celebrates the sixty-year legacy of the world’s greatest monster, Godzilla. 
• Kaijunited: Japanese Monsters & Us - A fan-made documentary focusing on kaiju fandom in the US, Japan, and France.
• Kaiju Gaiden - A crowd-funded feature that tells the stories of previously-unheard-of independent kaiju films, and the people who made them.
• SciFi Japan TV - A now-concluded online documentary series from the folks at SciFi Japan. The focus shifts per episode.

If anyone can think of or knows of any more, please give me a shout!