1. The opening scene with the giant actually has a bunch of other giants as well. It's a ritual, not a stealth seeding -- that point was ambiguous in the theater release. So he was considered an "official sacrifice" to seed the planet (unlike the original Prometheus, who brought fire clandestinely), it's clarified with this clip.
2. When they get into the chamber with the fluid in it, the one guy finds a large worm and puts it in a container while the others are nervous at first, and is all excited because they've finally found life. I think a common bitch about the TR was that the two guys treat a potentially deadly animal as if it's a toy/pet and how stupid that seemed; but this scene actually sets a precedent where their reaction might make more sense... they watched another similar animal be harmlessly captured earlier, but here they just happen to be waaaay wrong because the creature has been tainted at this point.
3. The scene with Vickers and Wayland where she utters some of her best lines ("A king reigns and then he dies") is expanded upon. Great scene -- she starts by apologizing for some past issue and he forgives her, so you think all is well, and then she comes in, says that to him, and the scene just becomes worse and worse until you realize she actually has nothing for him but contempt and cannot wait until his last breath is wrung from his body, in order to correct his breaking of the natural way of things. So it also makes sense when he dies and she watches on viewfinder and says, "Okay, let's go home." This scene also just really gives one the impression she's not an android (which some viewers kept trying to suggest she was).
4. The original take on the hookup scene between Holloway and Shaw is much more violent, I think... he's drunk and he really cuts her down to size where they argue about her need to believe and find humanity's roots, and he credits it (in a nasty way) to guilt over her mom's death and disillusionment over her dad's, so she slaps him hard twice and they have a wrestling match that results in him apologizing profusely (because he realizes what a dick he just was) and followed by hot makeup sex. This scene I felt was more powerful in the raw energy of it as well as what is driving her to find the Engineers....but it is lacking the nice side point of her being unable to bear children, which then makes the latter scene in the movie more horrific.
5. The prolonged scene with Wayland's speech to the Engineer, whereupon he is beaten to death with David's head -- it just makes more sense and is easier to follow when we get to hear what Wayland is thinking and why he thinks he deserves immortality.
6. Longer fight with Shaw and the Engineer, and she's taking an axe to him.
7. Nice scene with the captain and Vickers, in her private quarters, where he shares a relevant anecdote with her.
8. Alternate take with CGI effects of the "transformed crew member attacks people in the bay until fried to death" scene. Scott went with the human pre-CGI shots; I thought the CGI looked a bit cooler, actually.
more discussion about Shaw's faith and why it's important, and the different between her faith and her hubby's science. I think these scenes really would have helped the movie in terms of adding more depth to the discussion.
I forget what other clips there were, but those are some of the highlights.