You read “‘Well, I’m back,’ he said.” and close the book. Or do you? There is more if you just turn the page.
But why would you read material that isn’t part of the novel? If it was important, it would have been in the story. Allow me to offer some reasons.
If you were a history major in college, or just a history buff, the Appendices are full of the flavor you like. True, it is utterly invented history, but those of us who took a historiography class know how much “real” history is cobbled together from wishful thinking and guesswork. While imaginary, Tolkien’s histories, time-lines, and genealogies feel real, partially as a result of Tolkien’s skill as a writer and partly from the sheer depth of material.
If you love languages — the sounds, the complications of grammar, the etymology, novel orthography and characters, the joy you experience the first time you recognize a prefix or suffix in a foreign tongue — then LOTR has appendices for you.
If you want to know more about the characters whose adventures you’ve just spent so much time engrossed in. If you are interested in the biography of Aragorn, from his meeting with Arwen, his travels, on to the moment of his death; the doings of Legolas and Gimli; the careers of Sam, Merry, and Pippin, then keep reading.
There is more good stuff contained in the appendices. But if any one or more of the above is true for you, then by all means, keep reading past the Grey Havens.
A personal note. The HA, now twelve, decided she wanted to learn how to play table top RPGs. I did some research, found a Basic D&D clone that seemed age appropriate, and gave it to her for Christmas. Yesterday some friends came over. The HA ran her very first game, resulting in a TPK in the second encounter. I couldn’t be more proud. Totally remorseless, that one. Yes, she is still coming to grips with certain concepts and rules, but she ran her table with confidence.
Speaking of confidence, I am confident you ought to pick up a copy of Cesar the Bravo.