Aaah some fellow tolkienites here. Ahoy I tell ye!
My favourite book out of the Tolkien stable is undoubtedly The Silmarillion. Since a kid, I was always obsessed with mythology. I read up all about Norse, Greek and Roman mythology and simply loved the stuff. Then after reading The Lord of the Rings and the Hobbit, I started reading The Silmarillion. This book too is plainly put, pure mythology and great reading.
My favourite parts of the book? Tom Bombadil - there are theories floating around that Tom Bombadil is very possibly Eru Illuvatar himself. Here's what Tolkien himself had to say about him: "And even in a mythical Age there must be some enigmas, as there always are. Tom Bombadil is one (intentionally)."
Elrond said this: "(Bombadil) was not then his name. Iarwain Ben-adar we called him, oldest and fatherless. But many another name he has since been given by other folk."
What does he have to say about himself? This: "Eldest, that's what I am.. Tom remembers the first raindrop and the first acorn.. He knew the dark under the stars when it was fearless - before the Dark Lord came from Outside."
Here's a brilliant essay by Gene Hargrove, read it.
Other favourite parts: Gandalf's fight with the Balrog, from the deepest recesses of Moria to the top of Zirakzigil. Then the meeting with the Ents, and the Grey Havens where they meet Cirdan the shipwright, a great Elf.