Mark and I saw the extended version of the Fellowship of the Ring yesterday. I thought it was an interesting experience, because I was watching the same movie I've seen five or six times now, and yet there was something different about it. I'm glad that some parts didn't make it into the theatrical release, but others I think would really have improved things. In-depth discussion follows:
I've been a Tolkien fan since I was about six, so I don't have a good grasp on what the casual fan or completely ignorant viewer would and would not understand. So I can't judge what parts are good for boosting an understanding of the movie's events, but there were some parts that certainly fleshed out scenes that were quite weak in the original version. But let's start from the beginning:
The expanded intro was pretty spiffy. Few things were added, but watching Jackson's interpretation of the Battle of Gladded fields played out in greater detail was definitely worthwhile. Verdict: should have been included.
The 'concerning hobbits' preface was good in that it provided a comprehensive explanation about the Hobbit race overall, but I don't think it really improved the enjoyment of the film any. I think it ended up just getting in the way without adding anything other than background. Verdict: it was well to have been left out
The scenes in the Shire with Ted Sandyman arguing with Frodo and others (and Merry and Pippin singing) were true to the book and helped show that things were still going on in the Shire when bigger hijinks were ensuing outside. It also expanded on the relationships between the four main hobbits. Verdict: should have been included.
The various scenes between the Shire and Rivendell that added a few more frames onto certain parts I'm ambivalent towards. Might as well have left them out to save time.
The extra scenes in Rivendell are all fairly superfluous, even the ones at the council. Interesting, but unnecessary.
Finally, I think that Lorien was greatly improved in the extended version. Martin Csokas' performance as Celeborn was still as sad and wooden as it was in the theatrical version, but Cate Blanchett's lackluster scenes were augmented (though not improved in themselves) by more scenes in which she does a better job. And the gift-giving scenes helped explain a lot that went unsaid and ended up being slightly confusing later and in the second movie. Although time was a definite factor and Lorien used a lot of it, I think Jackson would have done well to have kept more of Lorien intact (though maybe cut down on the mirror scene, since I hate that part of the movie anyway

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As for the extra stuff, there was a lot of funny an interesting footage. I regret watching the part about how they hadled sizes, though; now that I know how they did it, parts of the movie have become somewhat less magical to me.
All in all, I don't think it's worth paying full retail price for. But it's definitely worth a rental, and serious fans will probably enjoy perusing Half.com or their local discount movie store to find a cheap copy.