BBC Radio version (incl. Ian Holm - 1970's) : Faramir's conversation with Frodo and Sam, the original conversation about "quality" of character. I mourn its loss in Jackson's movies...
In The Fellowship : Bilbo struggling to release the ring (you can see the strain in his fingers as he turns his palm) and then, after he has gone, when Gandalf reaches down for the ring, his fingers hovering over it and it appears to me that there is a flicker of a touch... and the soundtrack along with it!!! Phew, the tension!
And many a scene previously mensioned (apart from Gollum's schitzophrenia - irritating, gah, sorry!)