There are several Star Trek fan productions and I have seen quite a few, but by far my favorite is Star Trek Continues.
Here's a YouTube teaser for their third episode:
This episode is a masterpiece, taking what is arguably one of the top five episodes from The Original Series ("Mirror, Mirror") and expanding it in exactly the direction set up back in 1967, while being completely original in its own right. It was a daring move for the actors to go into this alternate universe where they had to move beyond the familiar and well-established characterizations of the "regular" universe, but they carry it off brilliantly.
At the helm and commanding with authority is Vic Mignogna, who both channels and makes his own the legendary persona of Captain Kirk. His additional credits include Executive Producer, Director, Editor, Writer and more, but it is his deft manipulation of the character owned so totally by William Shatner that garners my highest praise. It is truly a pleasure to watch him at work.
While that achievement is most impressive, equally impressive are the efforts of the production designers (the sets are perfect!), cinematographers (whose understanding of the original lighting schemes is beautiful), sound designers (who use the original music and sound effects with perhaps more skill than did The Original Series... wait, did I just say that?), and last but not least the actors, who all bring an obvious love for the source material and the original actors themselves, elevating their efforts far above the other fan productions I've seen. Of course Spock is my favorite Star Trek character of all time, and Todd Haberkorn is easily my favorite Vulcan since Leonard Nimoy (and there have been many pretenders to that throne). I am grateful that Todd got such a large amount of screen time in the latest episode, "Fairest Of Them All".
I cannot summon enough superlatives for Star Trek Continues, and I submit as evidence the fact that each of the three episodes produced so far has provoked an authentic emotional response from me. If you were engaged by the Star Trek Universe, and in particular have a nostalgic fondness for Kirk, Spock, Bones, Uhura, Scotty, Sulu, Chekov, and the rest of the Classic gang, you owe it to yourself to boldly investigate this series.
