Each part of the series The History of Middle-Earth has it's own special attractions. Here I intend to do what I didn't have time to do yesterday: consider them one by one.
The Book of Lost Tales, Pt. I and II, must really be considered as one work, separated by publication necessity, as was The Lord of the Rings itself. In these tales we see Tolkien in the first vigor of his creation, and the stories overflow with more humor, fancy, and poetry than his later style as it developed. The Lost Tales are, in fact, much closer to the spirit of The Hobbit than they are to the LOTR or The Silmarillion as it was later re-written. There is more of a note of enchanted wistfulness in the conception, as the English wanderer Eriol visits the last redoubt of the Elves and hears their long story. Tolkien later wrote in a more austerely serious manner (and it is great), but here his untrimmed inventiveness has Melkor climbing trees to steal the Sun and Moon, and the first conception of Sauron is Thu, a gigantic demonic cat. If I might use a conceit from the "legendarium" itself, it is like seeing the Valar at their mighty works of creation itself, and then seeing them withdraw further and further away until their hands in events are only guessed at.
In The Lays of Beleriand we not only get to see the longest examples of Tolkien's poetry and the most in-depth telling of the stories of Beren and Luthien (the tale closest to his heart) and the Children of Hurin, but we also get to hear the voice of his old friend, C. S. Lewis, writing notes on what he's read in mock-scholarly style, and even offering his own (mostly inferior, in my opinion--and I love Lewis dearly) re-writing of some of the poetry in his own style. It is Lewis and Tolkien at the height of their friendship, and a fascinating glimpse of a time for anyone who is interested in the Inklings, as I am.
The Shaping of Middle-Earth contains The Quenta Silmarillion, which is in effect the first version of The Silmarillion, and is, as it were, the stepping stone between the Lost Tales and The Silmarillion as it is published. There is also the Ambarkanta, in which the shape and nature of the world of the stories is discussed and outlined (including the question of it's flatness or rotundity); and the Annals of Beleriand, an early timeline of Elvish history (some of it in Anglo-Saxon). It can be a little dry, but it is intriguing for the scholar of Tolkien, and filled with little grace-notes like: "West, North, and South they spread and wandered, and their joy was the joy of the morning before the dew is dry, when every leaf is green."
The Lost Road is titled after the oddest work in the volume. This book contains the workings on the story of Numenor, Middle-Earth's Atlantis; more annals of Valinor and Beleriand, etymologies and discussions of the languages of Middle-Earth, and The Ainulindale, a new development in his concept of the Creation of the World. But The Lost Road arose out of a conversation Tolkien and Lewis had, where they expressed the feeling that there weren't enough stories of the kind they liked, and that therefore they should write some. Lewis chose space travel, and so his famous Space Trilogy began: Tolkien took time travel and started this tale that was never completed. In it the hero is born back in time, it seems by language and hereditary memory, from contemporary to Anglo-Saxon England and back to Numenor. What is peculiar about it is that it is Tolkien writing in a serious mood a story that begins in modern times, albeit with unusual people.
The next four volumes (The Return of the Shadow, The Treason of Isengard, The War of the Ring, and Sauron Defeated) comprise a sub-set in the series. They are The History of the Lord of the Rings. Here we can see Tolkien trying to figure out what "really" happened to Bilbo after The Hobbit, how Bingo (first Bilbo's son, then nephew, and ultimately to be re-named Frodo) came to have the Ring and start his adventure, meeting Trotter (at first a hobbit, then a human ranger, and then re-named Strider), and being menaced by "giant Treebeard," a villain at first. From at first being thought of as "the new Hobbit" and a fairly short adventure, the tale "grows in the telling" under Tolkien's increasingly steady grip, needing fewer and less drastic re-writes. The last volume, Sauron Defeated, includes not only the last part of The Return of the King, but also the story of The Notion Club Papers, the story of a fictional group based on the Inklings but set in the (then) future of 1980-1990, but found in 2012, and another look at the story of Numenor.
The next two volumes, Morgoth's Ring and The War of the Jewels, cover new re-writings of the Silmarillion material, worked over in the wake of the completion of LOTR. Morgoth's Ring is interesting for me particularly because it contains contemplations on Elvish marriage and naming traditions, and a story dealing with the differences between Elvish and human points of view on death and immortality. The War of the Jewels contains one of the longest prose tellings of the story of Turin, material that was later worked into The Children of Hurin.
The Peoples of Middle-Earth covers the composition of the Prologue and Appendices, and as such contains some lore and information that never made it to the final edit (including the fact that dwarf women do have beards). There are more essays on language and lembas. The final part of the book is The New Shadow, a story set in Gondor about 100 years after the Downfall of Sauron, in which the youth of Gondor, growing weary of peace, begin affecting orc-culture (not unlike some in Great Britain did with the Nazis), and a look at the coming of the men of Numenor to Middle-Earth from the point of view of the other men who had remained there.
There is a book I don't have, that I just found out about: The History of Middle-Earth Index. This is an over-all index, covering the entire series, and is apparently useful for following concepts and terms throughout the work. There is also a set of three gigantic tomes incorporating all twelve volumes.