First Contact Day comes to us from Star Trek: First Contact, originally released in 1996. First Contact remains one of my favorite Star Trek movies, and in fact movies in general. The pivotal ready room confrontation between Picard and Lily, and the bookend scenes with Picard and Worf, are some of the best moments in the franchise for me. Some fans had a problem with Picard in the movie because he's atypically aggressive, but you can go all the way back to the first season to see Picard acting lively, or his biography, which finds the younger Picard to be infamously impetuous (see: "Tapestry," or Nemesis).
The movie itself was originally released in conjunction with the franchise's 30th anniversary, along with the Deep Space Nine ("Trials and Tribble-ations") and Voyager ("Flashback") tribute episodes. In this 50th anniversary year soon to see the release of Star Trek Beyond, it's fun to remember twenty years ago how a crucial element of continuity was finally explored for the first time, one that had considerable impact on Star Trek as it continued to unfold over the next decade. Can Beyond match that, or next year's much-anticipated next live action series? Well, time will tell.