I consider myself a Star Trek fan. I've seen a few episodes of TOS, much of TNG, all of DS9, most of Voyager, and a bit of Enterprise, but I don't plan on seeing the new movie. The decision was made provisionally after seeing the original trailer, and nothing I've heard since has made me think my first impressions were wrong.
My first thought on seeing the trailer was "Why is this an action film? Did they get Michael Bay to direct it?" When coming up with adjectives to describe Star Trek, "Awesome" and "Extreme" are not at the top of the list. This isn't Star Wars. Trek has never been action/adventure—it's more exploration/diplomacy. In DS9, in the middle of all-out war, more time is spent on the internal politics of keeping the alliances together than on battles. If a ship fires at the Enterprise, the command is not "Return fire!" but "Open a channel." This is a show that spends screen time on staff meetings, for goodness sakes! Don't think I'm impressed by a trailer full of eye candy and people driving off cliffs.
I'm not thrilled about the use of time travel to hit the reset button, either. I've never been a fan of Trek's time travel plots, and I'd miss the canon. But that's fairly minor, and I'd still be lining up to see it, if it didn't have the wrong attitude. When George Lucas stuck politics and technobabble into the Star Wars prequels, they didn't fit. In a universe like Star Wars', senate proceedings and "midichlorians" stick out like a sore thumb. Similarly, dramatic action shots and people hanging off cliffs doesn't fit Star Trek's style.
Edit: The Onion, it seems, has summarized my complaints quite well: "Star Trek fans are decrying the new film as a fun and watchable action-packed thrill ride... There's not even one scene set at a long table where interstellar diplomacy is debated in endless detail."