My girlfriend has forced me to watch Star Trek, so now all of my vague knowledge about the show has become actualized.
Vaguely. I've watched four or so episodes, but I've yet to see an episode starring Spock or Mr. Sulu or Scotty. Apparently, in the first season of the show, they ignored all the characters whose names begin with the letter "S", in favor of Dr. McCoy and Captain Kirk.
Captain Kirk actually reminds me a lot of Odysseus, from The Odyssey. He's a good leader, in that he's very clever when it comes to getting out of dangerous situations. He's also a bad leader, in that his crewmates tend to be killed indiscriminately, and he pretty much ignores everything that his employees say. Except Spock. Sometimes he listens to Spock. (Mostly, whenever Spock agrees with him.)
I think the series would be improved, if it was a half-hour show, not a full-hour. Every episode I've seen has done at least one five-minute filler sequence, usually a countdown of some sort. I'll be tempted to just fast-forward through those in the future.