I wrote a nice long post yesterday only to have my browser crash before I could hit reply
Basically, Star Trek was excellent for its drama, and how the stories were set in the future yet dealt with issues like race and abortion and homosexuality in ways people could relate without them being in your face. Roddenberry's politics were of tolerance, yet not particularly left or right leaning.
On race, he had an episode where two races of people were at war so much they destroyed their planet. One race was left-half white, right-half black, the other right-half white, left-half black. It just pointed out how silly it was to hate people for the color of their skin.
Of course there was the first interracial kiss on TV (maybe the movies, too) when Kirk kissed Uhura.
In TNG, Troi was impregnated by an alien (in energy type form). She was basically raped, and the issue of whether to abort or keep the baby was a good part of the episode. She kept it.
In another TNG episode, a member of an androgynous race of people turned female and fell in love with Ryker (#1). Her race of people strongly disapproved of choosing gender and even had barbaric procedures to turn those few who fell out of line back into a unisex person. The story was clearly about homosexuality and how gay people have been forced to stay in the closet or face ridicule and hatred - and that people think they can somehow be converted one way or another.
The whole Federation/Klingon relationship strongly mirrored the USA/USSR one, even to the point where when the Berlin Wall fell the Feds and Klingons made an uneasy peace.
The crew of the original Enterprise was pretty radical for its time (1960s). Asian (Sulu), Black (Uhura), and even Russian (Chekov) serving together as if none of that mattered (it doesn't, btw).
There was no obvious need for money. The lack of drive for that somehow freed people to pursue bigger and better things (5 year mission to seek out new life and civilizations and to boldly go where no man has gone before!).
Yet the peaceful explorers were heavily armed and had no problem using those arms (phasers, photon torpedos, and more). The good guys used them in a moral fashion, while the bad guys used them for evil.
The drama was so good that the original series is still great TV even though it's just actors on a stage in front of painted backgrounds with cheesy special effects. It's the drama.
The thing is that Roddenberry is dead and the guys who took over the franchise afterward (Rick Berman in particular) really sucked at getting what made ST so great. The show Enterprise was really good, to me, but it wasn't even close to Roddenberry's work. It was basically just another Sci Fi show loosely based upon the ST genre. The show failed pretty miserably.
This is not to say that this movie is going to be bad. Lots of older franchises have made the jump and translation from re-run status to mega hit film or TV series. Batman was a corny TV show and has been remade as rather dark and action packed high tech films that are great. Battlestar Gallactica made the jump from corny TV show to a similarly dark and super high tech effects driven series that may be the best Sci Fi on TV the past few years. This movie could do the same for Star Trek.
FWIW, Stargate SG-1 stepped up and filled the void left by the demise of the Star Trek franchise. A number of people from the various Star Trek shows have appeared on it as well. In fact, the current leader of Atlantis was the holographic doctor on Voyager and one of the recurring villains was the engineer on Enterprise.
Lastly, how could a show go wrong with Denny Crane in his youth as the captain!