I think that the underlying story is good, and I also think that this film did a good job of converting it to the screen. Part of this may be due to the length, since the book is relatively short (170 pages in my paperback edition). I remember Harlan Ellison saying a few years ago that people should adapt novellas into films (rather than novels), since that way you don't have to cut bits out; I'm not sure which category this book falls into, but there was only one bit missing from the film which I specifically remembered from the book, and that may have been cut for other reasons (rather than to save time). By contrast, the "Harry Potter" films had to omit large chunks of the books.
There was an animated version of this story that I saw when I was younger, which I also liked, so I was surprised to hear people criticising it recently. However, I then saw a clip from it in an advert (one of the high street stores is selling it cheaply), and I was surprised at how ropy it now looks. Perhaps I've been spoilt by the improved special effects in recent years, but I think that the new film did a much better job. In fact, it may well be that this is a film whose time has come, i.e. you couldn't have made it this well until now. I believe that some of the books were made into live-action TV series a few years ago, but I didn't watch them, so I don't know how good they were. In particular, when I saw Aslan roar in the trailers I thought "Wow! 'Not a tame lion', indeed..." (to quote a line that is spoken frequently in "The Last Battle"). At the same time, he impressed me with his nobility and dignity in the film, so it's not as if he was portrayed as a completely savage beast.
I thought that the music was very good, and was also used in an appropriate manner. Specifically, it was very effective when one battle scene started in complete silence, to be replaced by noise (the impact of hooves and weapons), and then the music gradually came in.
Looking at the story itself, I think that there is a general theme of redemption. When Peter David was discussing the "Mary Poppins" film a while back, he said that the film is really about Mr Banks (the father), since he is the character who goes through the most change/growth during the course of the story. In the same way, I'd say that "The Lion, the Witch and the Wardrobe" is really about Edmund, since he learns the most from his experiences in Narnia.
Speaking of characterisation, I found it interesting that Susan and Peter were both trying to lead, but were doing it in different ways, and thus found themselves at loggerheads rather than working together. This reminded me of the family dynamics of "Charmed", where the sisters' personalities have been influenced by their relative ages. Digressing slightly, it was also interesting to see how the Halliwells adapted to Pru's absence, e.g. when Piper became the eldest one around, and therefore the de facto leader, rather than being the middle sister and the peacemaker.
I hadn't really thought of the books as being particularly funny (although it's been about five years since I last read them), but there were a few scenes in the film that made me laugh. I think my favourite line was the fox saying "I wasn't actually speaking to you", although that was one that made me smile appreciatively rather than actually laugh. There were also scenes that I found quite moving, so the film did a good job of stirring a wide range of emotions.
There are certain similarities between this film and "Lord of the Rings", e.g. they're both filmed in New Zealand with fantasy creatures. On the whole, I think that they're significantly different, but there was one particular scene in this film that did remind me of the others. This was when Peter, Susan, Lucy, and the beavers were hiding from the sleigh, so they were crouched in a ditch/cave with "the enemy" standing above and looking for them; the corresponding scene was in "Fellowship of the Ring", when the Hobbits were hiding from the Ringwraiths (who were on horseback).
The lead centaur also reminded me of Elrond, but that was just a physical similarity about the face, rather than in their personalities. Similarly, Jadis (the White Witch) made me think of Galadriel, but this is where the similarity almost goes in the other direction; it struck me that this is what Galadriel would have been like if she'd been corrupted by the One Ring, so the Narnia film actually made the Tolkien films better.
Regarding the White Witch, I think that the Queen in "Brothers Grimm" was better cast in terms of being very beautiful and simultaneously very evil. However, I think that Tilda Swinton is a better actress, and she was able to be convincingly fearsome.
shuripentu observed that Santa ignored the beavers; I'm assuming that this is because they're adults rather than children (in vague keeping with tradition). And speaking of tradition, I was interested to see that he was in a brown suit rather than the more familiar red one (despite Susan's later comment), which I think has a longer history (opinions seem to vary on the whole "was it just Coke's change?" question, and that's not really relevant here).
One question which occurred to me during the film, after Lucy first entered Narnia, was whether anyone else could go through the wardrobe door into the spare room, given that it was visible from the clearing. Maybe the Pevencies could offer asylum to Tumnus if Lucy took him back with her? There are various problems with this scheme, but it had never occurred to me to even consider it before. Is Jadis the only person from Narnia to make the return trip? (I have a vague feeling that Reepicheep may also have visited our world, but I'm not sure about that.)
More generally, I think it's fair to say that there are other stories which are more complex/sophisticated. However, I first read the Narnia books when I was quite young, and I've re-read them a few times since then (most recently about five years ago), so I have a lot of affection for them. I heard a comment from Philip Pullman a few years ago, where he basically said (paraphrased from memory) "When I criticised the books, I thought that I was just criticising books, but it turned out that I was actually attacking an institution", i.e. people took it quite personally.
Essentially, I'd say that the Narnia series as a whole contains classic middle class wholesome values. The film is true to this, since I'd describe the children as "very clean" (for want of a better description), in the tradition of Nesbit's "Railway Children". I think this is quite a widespread perception; for instance, in Ben Elton's novel "Inconceivable", he uses the books when he's portraying an idyllic view of childhood. There's a section where the narrator is describing his niece Kylie:
"I had last seen her about six months ago at a family do, and she had been a very sweet and pretty little eleven-year-old who had a picture of a horse in a locket round her neck. [...] We went on holiday with them the Easter before last and it rained all the time. Kylie spent the week lying on her tummy in front of the fire reading the entire Narnia saga. It was a lovely thing to see and Lucy and I had wished she was ours." [pp164,166 of paperback]
On a more personal note, I quite like the idea of a character called "Professor Kirk"! Also, when I was a student in Durham I often saw the lamppost near Prebends Bridge which was supposedly the initial inspiration for Lewis. In retrospect, I should have taken a photo of it in the snow while I was there, but never mind.
Having said all that, I think it's fair to discuss a few quirks of the film without claiming them as damning criticisms.
As I mentioned above, there was one scene that was notable by its absence - in the book, Aslan had to be quite stern with Lucy after the big battle, telling her to attend to the other wounded rather than staying with Edmund. I was also curious about whether her cordial would heal Edmund's face (minor cuts/bruises), which it didn't - I'm guessing that this was a deliberate choice rather than a mistake, and I can accept it, but I found it interesting (and thus noteworthy).
A more tricky aspect is the way that everyone looked to the children for leadership. This did remind me of the Harry Potter novels, particularly the statue in the Ministry of Magic (with non-humans being cheerfully subservient) which didn't match the actual human-centaur relations. In the Narnia story, the lead centaur clearly had more military experience, so I had to wonder what actually qualified Peter to take charge. However, I think that the key issue here was the prophecy. The books established that there are other humans in Narnia's world (even though they weren't seen in this film), so these four were specifically important in their own right, rather than on the basis of their species. The closest analogy I can think of is the legend about the eventual return of King Arthur.
I think the only part of the film that I was uncomfortable with was the hunt at the end. It could be argued that in Narnia there's a clear distinction beween the animals that talk and the ones that don't, but I'd guess that even the non-talking creatures would still feel pain. However, I'll cut them some slack here, since the Pevencies didn't actually catch the stag.
Lots of people have mentioned the Christian allegory in this story; there are clear similarities, but I think that the story stands alone (i.e. works on its own merit).
Regarding the saga as a whole, one other bone of contention is what happens to Susan in the future, as referred to in 'The Last Battle'. Basically, there's a line where Peter says "My sister is no longer a friend of Narnia". This was disappointing, since I like Susan, but I'm not sure that it counts as a failing of the books as such. For instance, if you look at Boromir (from Tolkien) or Anakin Skywalker (from Star Wars), they both started out well, and were later corrupted; I don't think that's an intrinsic flaw of the story so much as it is a failing of the character concerned. Neil Gaiman wrote a short story ("The Problem of Susan") about this, which has been published in the "Flights: Extreme Visions of Fantasy" anthology; I haven't read that yet, but I'd like to. See also "Lipstick on My Scholar"; it's a long article, but not as long as it looks when you load the page, because most of it is comments from readers after the article. It's interesting, and the key point is that Susan wasn't a bad person because she became interested in make-up/boys, but rather because she pursued those interests to the exclusion of all else.
Anyway, all in all I think that this was a very good film, and I look forward to the next one in the series. Apparently this will be "Prince Caspian" in December 2007 (although that information comes from an unconfirmed source), which I think makes sense; "A Horse and his Boy" and "The Magician's Nephew" can both be left until the end.