The first time I saw the commercial showing Gandalf opposing the Balrog at the Bridge of Khazad-Dum, I got chills. I STILL DO. The visual appearance of Jackson's interpetation is, to me, the quintessential version of LotR. I know some things are different, but that's as much a change due to a different medium as anything else.
And I'm going to a put another heresy out there, parallel to Henry's: I think the movie does some things better, for me. The series has many slow moments that, while good for a mythic poem or a romantic tale of old, don't really work as effectively as they might for the story being told. I realize Tolkien was working at different goals, but some of Jackson's choices (such as showing things happen that in the books are always told in flashbacks) improve the flow and pacing. The race for the Buckleberry Ferry, for example, is nothing like the book, but manages to deliver a lot of punch in a little time.
Arwen: well, since she has such a minor part in the books, I couldn't say.
Aragorn: not like I originally pictured him, but Viggo has made Aragorn his own...moreso than John Hurt, for example.
Gandalf & Saruman: Best. Casting. Ever.
Elrond: I thought he worked. The elves, in general, worked out well, but Celeborn was one of the characters who greatly benefited from extended release.
Hobbits: Not exactly the physical look I expected, based on appearances elsewhere (although not incorrect from my reading of the books, per se), but they worked all the same. All of the hobbits work well for me, but Sean Astin in particular seemed spot on for Sam, to me, in performance.
Gimli & Legolas: See Gandalf & Saruman.
Bilbo: Ironic that he once was Frodo, and now is Bilbo. A truly wonderful performance from a great actor. Spot on. The extended DVD really gives him some nice extra material.
Visually, Moria was better looking than I could have imagined. Lothlorien and Rivendell were spot on. The Shire was, IMHO, perfect and exactly as I had envisioned it. Weathertop was completely different, but the use of real location that unique made up for it.
I wonder if we'll get to see the WIndow on the West in TTT?