I saw an advance screening of the movie in Pittsburgh on 4/23/09 - here's some bullet point SPOILERS:
No Next Generation characters are mentioned or featured, but it fits in line with Star Trek Countdown.
Movie opens with Nero's coming out of a space/time warp and attacking the Kelvin, the ship that Kirk's father serves on. Nero defeats the Kelvin, and offers to let it survive if the Captain beams over to negotiate. He does, and puts Kirk's dad in command. Nero finds out that he is trapped in the past, and no one knows who Ambassador Spock is at this point. He kills the Captain, and Kirk's dad runs the ship himself until the crew can evacuate, including his wife and newly born son, Jim Kirk.
After the car scene with the young Kirk, and a scene on Vulcan with a young Spock, we cut to Kirk as a early twenties roughhouser who gets in a bar fight with Starfleet members over Uhura (who has no interest in Kirk), and Kirk gets a lecture from Capt. Pike who breaks up the fight, who knows who Kirk is, and dares Kirk to be better than his father, who himself is regarded as a hero in Starfleet. Kirk takes this to heart, and joins Starfleet, at the same time an older-than-Kirk McCoy joins, as his wife robbed him of everything but his "bones" in the divorce, so he joins Starfleet as a last resort.
Spock meanwhile has refused a position on Vulcan due to human bias, and joined Starfleet. We flash forward 3-4 years later, and Kirk passes the Kobiashi Maru test by "cheating", as he doesn't believe in a no win scenario (due to his father beating such a situation). It turns out Spock wrote the program as a teacher, and is "pissed" Kirk cheated to beat it. Spock, meanwhile is "sexually involved" with Uhura, a parallel to his father Sarek, marrying a human woman, Spock's mother.
Meanwhile, Nero awaits older Spock's arrival from the space warp, as Nero has waited 20 years for the Old Spock to arrive (a time distortion effect). It seems Old Spock and Nero are from the future of the Next generation, the regular universe, and in that time, Spock tried to save Romulus from a solar supernova using red matter to create a black hole to suck up the star. As Countdown showed, Spock was late to do so, and Romulus was destroyed, as was Nero's family. Spock then did stop the supernova, and the resulting space/time warp sucked old Spock's and Nero's ships into it. The future believes them all to be dead, but they actually warped into the past of an alternate universe/reality, and have now began interacting with this separate reality, effecting it. So this is not the past of the Star Trek universe we are familiar with, but a new one very similar but more advanced. Since Nero went in first, he comes out first, and old Spock comes out later (20 years later). Nero captures Spock and his ship,and uses his red matter weapon (which makes space/time warp) to use against Vulcan. He will then attack Earth, as doing so with not only allow Romulus to survive in this new universe, but also thrive with the Federation holding it in check. He drops old Spock off at an ice planet near Vulcan, so he can watch it be destroyed by Nero.
Because Kirk cheated on the test, and Starfleet hasn't decided what to do about that yet, he is not assigned to any ship now that he has graduated. Starfleet gets a distress call from Vulcan, and the Enterprise takes it maiden voyage there under Pike. Checkov, Sulu and Uhura are assigned to the Enterprise, as is Spock in 2nd Command. McCoy is also assigned, and sneaks Kirk onboard.
Based on the details of the ship that is attacking Vulcan, Kirk realizes it is the same on that attacked his father's ship back in the day, and convinces Pike and Spock to be ready for it. Nero ends up attacking, but offers to spare the E if Pike surrenders and beams over. Pike does, and leaves Spock in command, with Kirk as his 2nd.
Pike beams over, and is captured. He is tortured for info using Ceti eels (yes, from ST 2) to get info on Starfleet's defenses. Meanwhile, Nero has launched a drill platform that hangs over Vulcan, and is burning a hole to the center of Vulcan. Kirk, Sulu and a red shirt try to stop the drill, and succeed, but too late. Nero drops a red matter bomb into the planet, while Spock tries to save the Vulcan high council (including his father and mother) to save Vulcan's culture. Checkov beams Kirk and Sulu back aboard, and gets Spock and his father and some others, but loses Spock's mom in transport. Vulcan then collapses into a black whole space warp, and Nero head for Earth with every one left stunned and Spock crushed. Kirk tells Spock they should chase Nero and try to stop him, but Spock overrules this and says they should meet up with Starfleet's defense force. Kirk violently disagrees,and Spock nerve pinches him and drops him off on the ice planet near Vulcan,and warps to meet the fleet.
McCoy berates Spock for dumping Kirk, saying they should put their star horse int he stable. Spock, of course, counters his argument, which p!sses McCoy off just like it used to.
Kirk arrives on the ice planet, and while running from a massive attacking alien, he runs into a cave where Old Spock is hiding for warmth. Spock is delighted to run into Kirk, but is confused why he is not captain of the Enterprise (having now realized this universe is different.) Kirk is weirded out that this old vulcan claiming to be Spock and also his friend ("bullshiat"). Old Spock mind melds with kirk and fills him in, and Kirk asks if in the universe he's from the kirk he knew knew his father. Spock says yes, and that his dad was his inspiration for joining Starfleet and becoming Captain of the Enterprise. Kirk, now jazzed, joins old Spock,and they trek to a Starfleet outpost on this planet. Once there, they meet the commander, Scotty, who was dumped there as punishment for killing his CO's dog while attempting long distance warp transport. Spock gives Scotty his equation to teleport to the Enterprise at a large distance while at warp. Old Spock refuses to go with them (as a precaution to avoid his past self). Old Spock tells Kirk that he must take command of the E, and tells Kirk that both he, and thus his younger alternate self, are VERY emotionally compromised by Vulcan's destruction, and that under a Starfleet regulation, he can be relieved from command if Kirk can provoke a reaction to prove it. Since Kirk is still No. 2 on the Enterprise, he will then take command. Kirk slyly mentions that using all this future knowledge is cheating like he himself has done), implying the Spock he knows wouldn't approve. Old Spock slyly dismisses this, by saying and "old friend" taught him how to cheat. Scotty and Kirk then beam aboard the E, and young Spock is startled they managed to do this. When he demands Kirk and Scotty answer how they did this, Kirk refuses to answer,and goads Spock to show his sorrow and anger at him. Spock flips over the grief and attacks Kirk. Realizing he crossed the line, he tells McCoy to relieve him from command,and Kirk steps up. The crew follows Kirk, but doubts him.
Sarek then tells Spock that he really married his mother because he loved her, not just smooth over his vulcan ambassadorship of Earth as he told Spock earlier. This reenforces Spock to grow closer to Uhura.
Kirk and the E catch up to Nero at Earth, and Spock comes on the bridge to offer his position as 2nd in command. Kirk volunteers to beam over to Nero's ship to save Pike and disabled it. Spock mentions that he would quote regulations that forbid the captain to leave the ship, but he knows Kirk would "just ignore him anyway".
Spock volunteers to beam over with Kirk, and Kirk and Scotty are surprised to see Spock kiss Uhura goodbye, especially Kirk, who couldn't get anywhere with her at all at the Academy (he couldn't even get her to tell him her first name, which is a running joke).
Spock and Kirk both beam over, and Kirk frees Pike while Spock finds the ship old Spock came from. Kirk tells Spock enough to let him know he has old Spock's help, and young Spock uses the future ship to attack Nero's ship, stop Nero's drill from drilling into Earth, and distract Nero into following Spock's ship, and the E far away from Earth's solar system. Nero attacks Kirk, and mentions he recognizes his face, and that Kirk was considered a great man in hsi universe, "but that was another life". Kirk defeats him,and beams himself and Pike over to the E. Spock crashes the future ship into Nero's and detonates the red matter on board. Spock is beamed over the the E, and the red matter makes a huge space-time warp that crushes Nero's ship. Kirk then offers to save Nero and his crew, who rudely refuses. Kirk them whispers to Spock that he thought Spock would appreciate Kirk's peaceful gesture to Nero (to smooth over any possible ripples with the Romulans) to which Spock replies "no, not in this instance". They then fire torpedoes at Nero's ship,and blow it to pieces.
But the space/time warp is too strong to break the E free from (even with Scotty giving it all she's got"), so Scotty come sup with the idea to dump the warp core,and detonate it, so that the shock wave pushes them free. It works,a nd the E is saved.
In the aftermath, Pike is promoted to admiral, in a wheel chair, but NOT scarred,and Kirk, due to his actions, is promoted to full Captain of the Enterprise.
Old Spock decides to meet young Spock. Young Spock wanst to quit Starfleet to help restore hsi race, which is done to 10,000 or less, but old Spock tells him to stay, as they can be in two palces at once. Old Spock has found a planet to start a new Vulcan colony, and old Spcok tells young Spock to pursue his friendship with Kirk and the crew,a s it will define him in great ways. Spock then watches the younger Kirk promoted.
The final scene is on the E bridge, where Kirk (in full captain's uniform), tells McCoy to buckle up, as the whole crew is on board,and the E warps out into space over the familiar "final frontier voice over, read by old Spock.
Personally, I had my doubts, but I loved it. The crowd I watched it with loved it. Each actor fits the roles perfectly,and are very "familiar" feeling. McCoy is flawless (creepy accurate, even), Quinto won me over as Spock, Pine as Kirk is a perfect fit and a great lead, Chekov was great, Sulu fit the bill, Uhura was good too,and Scotty was funny, but perfect. Just enough humor, but never corny. A LOT of mentions and nods to things in ALL the past series and movies. Very fast paced, GREAT special effects, and since this technically takes place in the past of an alternate reality, it doesn't void what came before.
It will make big money. Count on it. I recommend you read Star Trek - Countdown first. It fills in a lot of the future backstory.