There is a distinct difference between "playing the Dane" (i.e., "jumping the shark") and merely "channeling the Swan."
[Those sound like three different and complicated dives we'll see during the summer olympics this year, but they're meant to indicate ways of incorporating Shakespeare into a television show.]
Star Trek—whether original, next, or miscellaneous—frequently channels the Swan, but I don't think it can be said to play the Dane when it does so.
In the third season of Star Trek: The Next Generation , Data and Captain Picard work on a scene from Henry V. Though it's not the best Henry V you'll ever see, it's not too bad. In a later post, I'll show you a Henry V to decry to the ages!
In the meantime, try this scene on for size:
Links: The epidosde at IMDB. The epidosde at Wikipedia.