"Trials and Tribble-ations," a fifth season episode of the STAR TREK DEEP SPACE NINE TV series, aired on November 4, 1996. Using technology pioneered by Robert Zemeckis' FORREST GUMP movie two years earlier, the DS9 special effects technicians were called on to plunk the cast of the show in an original series 1960s episode of STAR TREK. Not just any episode, mind. It was that "Trouble with Tribbles" one -- the one that everyone and their Mom has seen at least a couple of times.
Here is a Sci Fi Channel documentary about the behind the scenes work.