The most noticeable omissions to me were 1) The Scouring of the Shire (mentioned above) and 2) Tom Bombadil (I assume will be mentioned in a future installment :)).
Leaving out Tom Bombadil is understandable but leaving out the Scouring of the Shire was inexcusable to me. It seemed like such an important part of the book.
Yes! It took a lot of the hobbits credit away. It would have been amazing seeing Frodo and company fighting Saruman (Sharkey) all by themselves.
Also, there's a huge omissionn which would require more than one post: The Silmarillion. Although a full and huge story by itself, I just can't imagine a way in which all the totality (even if it were summarized) of this work could be bring into the big screen.
It seems REALLY unlikely but hey, we have to keep dreaming. Who knows? :)