Today some of it seems really dated, but you have to put it in perspective. The show was conceived at the beginning of the 1960s and the first episode aired on September 8, 1966, nearly three years before man set foot on the moon. In fact, the series was over before the first moon landing. I remember what it felt like back then. There was a feeling the human race could do anything it set its collective mind to. A permanent base on the moon seemed like it would happen within a decade or so, definitely before the turn of the century.
Look at the colourful thingys Spock is always slotting into the ship's computer. Can you say floppy disk? How about the communicator -- the cell phones we use every day were inspired by it. A multi-racial main cast was unheard of at the time, yet Trek did it.
Many of the episodes tackled difficult issues of the day. The Vietnam War was a growing issue; Trek took it on in
A Private Little War, where Kirk and the Klingons engaged in an arms race on a previously peaceful planet. They took on racism and other issues in the midst of the greatest social upheaval in American history. The writing was at times as brilliant as anything that had ever been seen on TV up to that point.
Star Trek paved the way for the other Trek series and movies, and for shows like Babylon 5. Without it, imaginative fiction on TV would be far, far different, and I venture to say, quite possibly far less interesting and entertaining.
May the original series live on forever!
-- yes, I have a life size Spock cutout next to my desk, just ask Dawno, she's seen it on my webcam. 
