First of all, the background story you need to know to fully appreciate the movie (no spoilers):
10 years or so after Star Trek: Nemesis, the Hobus star deep within Romulan territory explodes. For reasons known only the physics of Star Trek, instead of weakening as it expands, Hobus strengthens as it absorbs matter like its planets. As a result, it threatens to destroy nearby Romulus as well as ultimately the entire galaxy.
Both Spock, now openly the Federation ambassador to Romulus, and a non-descript but patriotic space miner named Nero, realize the danger but their attempts to warn the Romulun high council fail. Spock notes that the Vulcans have developed a technology that allows them to convert decalithium, a rare mineral that Nero just happens to have lots of in the hold of his ship, the Narada, into red matter, something that can shut down an exploding star. So with the assistance of the U.S.S. Enterprise-E under the command of Data (his engrams having been uploaded into B-4's frame), Nero and Spock go to Vulcan. Despite the help of Federation Ambassador Jean Luc Picard, they cannot convince the Vulcans to help the Romulans either.
Nero gives the decalithium to Spock who secretly whips up some red matter and promises to do his best to help save Romulus. While working on this with Geordi Laforge who has created a small ship called the Jellyfish to approach Hobus without getting all burnt to a crip, Nero returns to Romulus in time to see it destroyd by the expanding Hobus.
The trauma of seeing his world, along with his pregnant wife, incinerated, drives him mad. He and his crew promptly shave their heads, cover themselves in tatoos and swear vengeance against:
a) Spock, for not helping promptly enough
b) Vulcan, for not helping promptly enough
c) the Federation, because they didn't push the Vulcans enough
Meanwhile Spock finishes his preparations and takes the Jellyfish to Hobus where he pops the red matter into its core. The plan works, a black hole is created which sucks Hobus into it, ending the threat. But Spock cannot escape as he is caught in the gravity well of the singularity. Just as his ship is about to get sucked into the black hole, the Narada shows up to destroy him but before Nero can fire, his ship is also sucked in. The Enterprise arrives to see both ships disappear, sad at the loss of Spock but happy that Nero is also gone.
Until the movie starts, that is...
Review (warning: spoilers)
Overall I thought it was excellent. The plot is a bit weak but the point of this movie isn't to leave you scratching your head and wondering at the profound dialogue, but to walk out of the theatre with your ears ringing and your mind wondering at the amazing special effects and how, with a simple little trick, JJ Abrams has managed to wipe out 40 years of Star Trek history and give himself a blank slate to recreate the franchise, without affecting the original canon!
See, here's the trick: By emerging from the black hole at the moment of James T Kirk's birth, Nero changes history. Kirk is raised completely differently, most other major characters have altered time lines and the circumstances that bring them together are completely different from the first time around. And that means the possibilities are now endless without having to create a different crew.
The casting was inspired. Chris Pine does an excellent version of what a young and undisciplined Kirk would have been like. This is cast in even sharper relief when one remembers descriptions of Kirk at the Academy ("Where No Man Has Gone Before", "Shore Leave") as being humourless and a compulsive bookworm who was constantly the target of practical jokes and couldn't get a date to save his life.
Zachary Quinto, who I hate as Sylar for being so petty and one-dimensional, shows an alternate Spock in which his emotions aren't entirely so surpressed. For those who wonder why it's Uhura of all women that he's getting it on with (poor Nurse Chapel!) watch "The Man Trap" again. Clearly this relationship is a reference to an awkward and (thankfully) nearly forgotten scene from early in TOS history where Uhura shameless flirts with Spock on the bridge, while on duty.
(Fans will recall that Uhura was dating Scotty during the events of "The Final Fronteir". Slut)
Scotty, Sulu and Chekov are also fun to watch in their slightly altered versions. It's a bit disconcerting to see Sulu played by a Korean but I guess his daughter, Demora, who was also mysteriously Korean, had a retroactive effect on his genetic struture. Or something like that. (or could it be that all these decades later, Orientals still all look the same to Hollywood brass?)
Karl Urban, in my mind, is the standout though for not trying to reinterpret or update his character but doing an amazing job simply channeling DeForest Kelly back to life. My God, Jim, I haven't seen anyone recreate a dead actor like that since Man on the Moon. When he shouted "Dammit Spock! I'm a doctor, not a physicist!" the doubts are dispelled.
There are also enough "in jokes" to keep die hard fans happy. We learn where McCoy's "Bones" nickname came from. We get to see the Kobiyashu Maru simulation although Kirk's obnoxious behaviour during the test was a little too much for me. Remember that in the original time line his effort to successfully rescue the ship was not detected as cheating and that he received a commendation. This time he comes off as a spoiled brat and not sympathetic at all.
However when Spock quotes from Sherlock Holmes ("Once you have ruled out the possible...") just as he did in "The Undiscovered Country", and after the scene in which Quinto meets Nimoy and again exchanges a classic quote, this one from "The Wrath of Khan": You lied! I implied! the torch is passed. We can await the new adventures of Pine and crew with great excitement.
(You think he'll get that green Orion girl as his new yeoman?)
1) A gigantic ship emerges from nowhere and, within a few minutes, destroys a Federation starship. And Starfleet's response? You'd think they'd mobilize the entire fleet and hunt this thing down. Nope.
2) Survivors of the Kelvin would surely note that the Narada was severely damaged when the Kelvin rammed intself down the ship's throat. Why no computer directive like: If you encounter this ship, here's what you do to destroy it? Why is its appearance to the Enterprise at Vulcan a complete shock?
3) Spock announces he must go to the Narada because he has the best chance of figuring out their computers since Vulcans and Romulans share a common heritage. Remember from "Balance of Terror" that Vulcans did not know anything about Romulans until that first feed from the cloaked Bird of Prey's bridge. Spock was completely surprised by Romulans' appearance. So how could he know about this shared heritage?
The Jewish angle:
I only wish I knew gemara like I know Star Trek (he said, hanging his head in shame... briefly)