A number of humorous Star Trek-references have recently surfaced, besides the Monty Phyton and the Holy Grail parody. Some are direct references such as All-Ages Kirk/Spock Archive, and some deal with Star Trek content as part of other issues, like the "White and Nerdy" video by Weird Al Yankovic (quiz!).
But these outsiders have serious competition by none other than the series themselves. From Captain Picard singing the Alphabet of Love, to a whole documentary piece devoted to humor and bloopers, hosted by William Shatner: