It looks like someone got their hands on the original script for Star Trek XI. As reported by TNMC, there were several scenes that didn't make it into the final movie.  Who knows if any of the scenes were even filmed, but they are most definitely in the original script.  Check out the descriptions below.

Right off the bat, we have a scene where Spock is born.  The thrust of the scene is Spock's mother Amanda expressing her displeasure with Sarek when he isn't present for the birth and then doesn't understand the emotional implications of this.  One gets the feeling that this probably happened an awful lot in this relationship.  The script then jumps to the scene where Kirk is born, which is where the movie opened.

The opening sequence, which sees the destruction of the USS Kelvin at the hands of Nero and his mining ship the Narada, has an extra bit we didn't see.  While the Narada is trying to recover from being rammed by the Kelvin, bunches of Klingon warbirds decloak and surround it.  This leads to a major subplot entirely removed from the final film.  More on that later.

We get a couple of scenes that precede the part of the movie where young Kirk takes a Corvette for a fateful joyride.  One shows his older brother storming out of the home of their Uncle Frank, who is clearly not meant to be a nice guy.  Mom is apparently in Africa and not expected back for months.  Older brother George leaves home, implying along the way that Jim is too much of a rule follower.  The next scene shows Jim washing that Corvette under orders from his Uncle.  I'd say this section was wisely cut as it adds nothing truly important to the story that isn't conveyed in the joyriding sequence.

Next we go the Rura Penthe Klingon Prison Asteroid where Nero and his crew are being held.  The Klingons catch someone trying to smuggle Federation maps to him.  The Klingons begin to interrogate Nero, during which we learn that he has been there for ten years and hasn't said a word that whole time.  The Klingons have a notebook of his that is full of drawings and calculations relating to Spock and his Jellyfish ship.  They decide to use that slug thing we saw Nero using on Captain Pike in the finished film.  Apparently they hate being in the dark and will claw their way out of any dark place they're put, which makes them kind of bad to have in your gut.  Nero tries to deal with this torture by focusing on memories of his late pregnant wife.  A few scenes later, we see that Nero is so bad ass that he put up with torture just because he had time to kill until Spock finally arrived in the Jellyfish ship.  When the time is right Nero busts out with ease.  It's possible this subplot was cut for plausibility issues.

Quick side note.  The explanation for McCoy getting the nickname Bones is not in this script.  I'm not sure where it did come from but it's better than what the script has.  Good choice there.

The scene where Uhura catches Kirk fooling around with her room mate has a little bit we didn't see in the final film.  Kirk tells Gaila that he sent her a message that she has to open at a precise moment.  This is how he hacks the Kobayashi Maru test.  It is a virus of sorts that she opens during the test, unleashing it to rewrite the test to be winnable.  I'm not exactly sure why this was pulled.  The sequence makes a bit more sense like this and would only be a fraction longer.  There is one more scene later where Kirk mistakes another green girl for Gaila.  This was wisely cut.

The sequence where Nimoy (referred to as Spock Prime in the script) and Kirk meet on the ice planet is more or less the same as in the final film.  But there is a line of dialog that addresses the massive improbability of them meeting like this.  I'd say cutting that was a mistake.  It would add only a few seconds to the film but eliminate a moment that could easily pull viewers out of the movie by being hard to accept.

There is a scene as the Narada approaches Earth in which Nero's second in command, Ayel, threatens mutiny.  He intimates that the crew feels destroying Vulcan has gotten them revenge and they now want to simply return to Romulus, which at this point in time still remains.  Nero understands the crew's desire.  But he will not return until everyone involved in the destruction of Romulus is punished.  He kills Ayel and orders the drilling into Earth's crust begin.  This is pretty major since in the final film, Ayel doesn't die and continues to be involved in events during the climax.  It's a nice moment that gives Nero more depth.  I suspect it was cut for pacing reasons.  Too bad.

The sequence where Kirk and Spock beam on to the Narada has a little extra bit where Spock gets cruelly violent to Romulans at Kirk's order.  It's an unattractive moment, best forgotten.  It was replaced with the nifty gun battle where the effects guys made the Federation phasers very cool.  Definitely a change for the better.

Finally, at the end of the script is provided an alternate take on the scene in which Spock and Spock Prime meet.  Before saying goodbye, Spock Prime hands Spock a locket.  Spock activates the locket and sees a holographic video of Kirk, and by that I mean Shatner, singing happy birthday to Spock and congratulating him on becoming an ambassador.  The message continues, basically telling Spock that the two of them should get back together one more time with a starship and just... explore.  It's a nice idea but I can see any number of reasons it was cut like pacing, being overly sentimental, Shatner not being interested or simply recognizing that by this point in the movie this new version of old favorites have earned the right to stand on their own.  Whatever the case I think the movie is just fine without it.  Better even.  They are rebooting Trek here.  Leaning too much on the old Trek is just a sign of weakness.  Leaving this out is a sign of confidence. (source TNMC)

Let's hope at least a few of these were filmed and make on to the deleted scenes section of the blu-ray.

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