My verdict after stewing it over for a few hours: Good, but not great.
I’m a long-time Trek fan, but I don’t mind the “alternate universe” thing one bit. If they wanted to restart the franchise using the TOS characters, they needed to find some way to disregard the bloated mess that Star Trek’s canon has become (and I’m speaking here as a hardcore fan of DS9). If they don’t, you end up with “Enterprise.” 
In fact, I would’ve been fine with a straight-up reboot that ignored canon entirely once the basic characters were established. Seeing Nimoy back in character was a lovely treat, but his presence over-complicated the story in (IMO) an unnecessary way. I’m loathe to use the word “shoehorning” for something as purely wonderful as getting to see the original Spock one last time, but it did feel that way at times.
But that’s sort of a running problem throughout the movie - the plotting is just plain bad. And I don’t mean the bad science (although there is plenty of that), I mean in terms of storytelling mechanics. Telling rather than showing. Towering leaps in (il)logic. Plot holes you could drive a Warbird through. And some of the craziest coincidences I’ve ever seen anyone attempt to pass off as story progression - Kirk randomly running into both OldSpock and Scotty, the exact two people he needed to meet in order to move the plot forward, being the most egregious. The black hole-generating goo was another in a long line of ludicrous hand-wavey Treknobabble. Several of the action sequences could’ve been cut from the movie in their entirety without affecting the story one bit. The ice monster, in particular, felt like a cut scene from the Star Wars prequels, while Scotty’s Wild Ride through the pipes in Engineering felt like a level from the admittedly-nonexistent video game adaptation.
Another issue I had was with the villain. Nero was well-played by Bana, and has one of the funniest moments in the movie (“Hello, Christopher! I’m Nero.”), but the character is appallingly underwritten. Yes, I know there’s a comic that explains his backstory in some detail, but if you want an audience to react emotionally to backstory, you had better work it into your movie somehow. “It’s too complicated” is no excuse - either find a way to explain it simply and coherently, or rewrite the damn thing so it doesn’t require 30 pages of exposition to understand. Khan’s origin is no less complex than Nero’s, but we’re given enough explanation (and Khan is given enough screentime) in Star Trek II that his motivations are crystal clear, even if you’ve never seen “Space Seed.”
So that’s a lot of stuff I felt didn’t work in the movie. And yet, I think overall it was very much a success. So what did work?
Well, they nailed the single most important factor: the main characters were spot-on. Although Abrams et al apparently can’t plot their way out of a paper bag, they can write some darn good dialogue. They were ably assisted by the talented cast, who thoroughly embody their characters without aping their predecessors. Most importantly of all, the “core trio” crackled with energy and showed striking chemistry from the moment they began sharing screentime. I can’t wait to see the Kirk/Spock/Bones relationship developed further in the inevitable sequels.
The supporting players were generally great as well. Chekov and Scotty were both entertaining without being annoying, although they’ll need to take care not to Wesley Crusherize Chekov in the sequels. Saldana’s Uhura is a much more assertive and interesting character than the original. I have a feeling she’s not going to settle for endless repetitions of “Hailing frequencies open,” and good for her. Harold’s Sulu made less of an impression, although he got off a few good one-liners. I admit this may be just me - it somehow doesn’t seem like Sulu without Takei’s voice.
The special effects were, for the most part, fantastic. I still think the new Enterprise design looks remarkably silly - it’s great until you get to the engineering section, and then the whole thing kind of devolves into Steve Jobs’s worst nightmare. But the space battle sequences were very effective, particularly the opening with Kirk’s father. I especially liked how the sound abruptly cut out whenever the camera began following crewmembers in space, starting with the hull breach in that opening battle sequence.
The hand-to-hand combat fared less well, mostly due to some questionable directorial decisions. Sulu’s “Wesley from Angel did it first” sword was silly enough. But falling prey to the Star Warsian giant chasms of doom in fight scenes aboard the Romulan ship? Oy.
Final thoughts: Star Trek '09 was witty, well-acted, and (to borrow Scotty’s phrasing) ex-CIT-ing, but whoever came up the plot should… ah… probably be replaced. I’ll have to see it again to be sure, but right now I’d rank it after Star Treks II, IV, VI, and First Contact - in other words, in the upper-middle of the Quality Continuum ™. The most important thing in my mind right now is that, for the first time in a long, long time, I’m excited to see the next adventure of the Starship Enterprise. If they can maintain what worked, and tweak the stuff that didn’t, we should be in for quite a ride in those inevitable (but not in a bad way!) sequels.