Ok, I agree with a few typings, but the majority I've seen so far are a long way off for me. I'm going more by the books, because numerous characters in the films were either given a completely different role and personality or simplified quite a bit to save space and change focus.
Here's mine, with a few explained in greater detail. If anyone wants me to justify an individual typing I'd be happy to have a go, it's too much work right now to provide a rationale for the lot, so I'm just going to note a few special cases:
The fellowship
Aragorn: ENFJ
Gandalf: ENTP (there seriously is no TJ about the man/wizard/maia! Very little forward planning in his leadership, and not much fondness for taking a leadership role at all, he generally only does so when pushed into it by others: his preference is for inspiring others to do the right thing by spreading his own wisdom, and setting a positive example with his own actions)
Frodo: INFP
Sam: ISFJ
Gimli: ISTJ
Legolas: Hard to be certain, but could be ENFP - this makes the unlikely friendship of opposites with Gimli gain significance too; they're probably opposite personalites as well as races.
Boromir: ESTP (ESTJ? Seriously, ppl!)
Merry: Seems like an Se dominant type in the movies, but the characters of the two younger hobbits are altered quite a bit for comic relief purposes. In the books it's hard to be certain, but he seems most like a mature ENTJ overall. He shows a lot of imagination and decisiveness when in a leadership position, most notably in the battle at the end of the book.
Pippin: Probably ESFP The N/S balance doesn't seem all that certain though.
Other characters
Theoden: ESFJ
Eomer: xSTP I'm not sure on the E/I balance, he seems slightly more E overall but seems to have quite a strong Ti.
Eowyn: ISFP Classic ISFP-ness!
Denethor: INTJ? (but could easily be INFJ; what's obvious more than anything is a lack of effective judgement of any kind as his Ni fuelled paranoia spirals wildly out of control)
Faramir: INFP (yes, a mature one!)
Arwen xNFP, she may seem more definitely extraverted in the movies.
Galadriel: ENTJ (This is much more obvious if you follow the course of her long life through Tolkien's other writngs. She's a dominant personality who loves to rule and create her own vision of order and perfection, she seems to be motivated by this above all. We mustn't take her refusing of the ring too lightly, it really is the ultimate temptation to her, and her rejection a sign of final maturity, coming to terms with her own nature and realising that the quest for ultimate power, if fulfilled, would make her no better than Sauron himself.)
Gollum: I'm not so sure we can type the crazies! I'm not even going to attempt him right now.
The riduculous Bombadil is definitely Ne dominant, probably ENFP
Bilbo seems quite ENFP too. Ne dom again in any case. It comes across more strongly in The Hobbit though.
Elrond is hard to type, but I would go with a mature INTx, with INTJ being first choice (he's been around thousands of years, he should be mature by now!)
Sauron is an obvious ExTJ but I'm not so certain which. He actually displays characteristics of both types at various points (more obvious in the Silmarilion and Tolkien's notes). In comparison to his very obviously ENTJ master Melkor (of whom Sauron was for a long time only a servant) he seems much more S. He's far more pragmatic and limited in his goals and only wishes to control the outward actions of others, in contrast to Melkor who ambitiously wished to bring the very substance of the world under his dominion. He seems also at times to not be very flexible in his thought and to stick rigidly to his preconcieved notions, as in his management of the war and total failure to project himself into the minds of his enemies. On the other hand he displays imagination and flexibility in bringing about the downfall of Numenor and infiltrating the Elves to learn the secrets of their rings. I can't decide either way.