anyone who has read and enjoyed lotr should do themselves a favor and read the silmarillion.
in reading the books, you will begin to understand the amount of depth and reality to middle earth, but when you read the silmarillion, you will understand that middle earth was a place that might as well have existed. tolkien created an entire universe and history, and the depth and reality of it blows the mind.
reading the silmarillion will make you appreciate the lord of the rings so much more. there is much in lotr that seems to be just normal narration or description, but actually has base in history of middle earth (and not just middle earth the continent, but all of arda).
after reading the silm, when you re-read lotr many things will pop out, and you will have a greater understanding, and a much greater appreciation for lotr, and tolkien in general.
the silm is essentially a collection of smaller stories, all tied together in progression and time, but each of these stories carries so much power and influence. he lay of leithien (of beren and luthien) is i believe the greatest and most powerful story ever told. it is a legendary epic, greater than that of any other literary work i know.
i started to type out a summary here, but stopped, lest it be spoiled by my telling.
it takes up many pages of the silmarillion, but is nowhere near novel length. i live in hope that someday, someone will re-write it in full length, as was done in the story of "isuldur" which was written in great detail by another auther, true to tolkiens work.
as to the questions addressed in the origional post of the thread, the elves do indeed go back to valinor, though it was removed from arda. and tom bombadil is an enigma. tolkien himself claims to not know who and what bombadil exactly is.
the adventures of tom bombadil is essentially a small collection of stories/songs/poems about him, but really have no relevance to the happenings of middle earth. i believe they exist seperately, and on their own.
the true mysteries of tolkiens works are answered
here though, and should only be read by those who have at least read lord of the rings
(some of them require silmarillion knowlege)