For me it changes all the time. One time when I read the book I couldn't stand it when I was reading about Frodo and Sam. However, when I re-read the book this year I really enjoyed it.
Me growing up also changed it a lot. At first like many of you I read LOTR for the story. Now as I've grown older I have re-read the book not only for the story but also for character development etc. So now there are very few parts that I do not enjoy. Although I have to confess that when I read the book this year I did skim read the Palantir part in The two Towers. This time around I thought that it was tedious. But next year...I might just enjoy it.
As for The council of Elrond,every time I approach the chapter with dread because I think it will take me a long time. It usually turns out that I read it in a jiffy.
