The "odd-numbered" Star Trek curse has finally been lifted. This Star Trek is hands down the best one ever. There are still some corny lines, but all the actors did a great job capturing the essence of the original crew. The time travel aspect was weird, but I'm guessing the writers did that to set up for future ST movies so that die hard trekkies would not complain about plot inconsistencies in the future.
I've talked to people who had never seen ST before and loved it, so I think it has broad appeal. You definitely don't have to know anything about the series to enjoy it, though it might be worth watching ST II: The Wrath of Khan to appreciate some references made in this movie.