Didnt skip anything as such, but my least favorite part is Frodo's and Sam's walk from Cirith Ungol to Mount Doom. Nothing much happens there, they get thirstier and thirstier, the ring gets heavier and heavier, Mordor sucks, Lembas is running out - he just repeats these two things endlessly
I think instead he should have cut the walking stuff to a few paragraphs, describing how thirsty and all they are, and used the space for a long interesting adventure, giving some more hints at "Life in Mordor" + hinting at some old secret stuff, like they come acrors the stables for another kind of fell beasts or somehting, to steel some food there from Orc WOMEN, as well as nick some gross mysteriously descibed animal to ride on using the ring to control it.
Caradhras is boring also.
Fav parts are: All the mysterious things and places (Bombadil, barrows, Moria, paths of the dead) + council of Elrond.