Over on the website TNMC (via AICN), they have up a review of the Star Trek shooting script which picks out and describes the scenes that didn't make the final cut -- scenes that were probably shot and cut for a number of different reasons (pacing, running time, etc ..), but will hopefully arrive on the DVD. It's a shame, too, because some of these scenes seem to address my main problem with the movie: the boring villain, Nero (as played by Eric Bana). The scenes in question (which involve an entire Klingon subplot!) appear to give Nero more depth as a character, so hopefully we'll get to see them eventually. Here are a few descriptions from the site:

"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."

"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."

Read more at SciFi Squad