What are the differences between Holmes, Moldvay, and Mentzer D&D? Also, which one came first?
D&D started as a series of little booklets, now called "original D&D" (OD&D). These booklets were basically barely-edited versions of the house rules of Gary Gygax and Dave Arneson.
In 1977, TSR hired J. Eric Holmes to develop a Basic D&D game. This was a dark blue, boxed set containing D&D in a single book, plus a module (B1 In Search of the Unknown), and some dice (or cardboard chits, when they ran out!).
Moldvay and Mentzer are game designers who took the old Basic D&D game (edited by Eric Holmes) and revised them. Both produced "red box" versions of the game. You'll find far more differences between Holmes and the later red boxes than you'll find between Moldvay and Mentzer.
Tom Moldvay revised the "Basic" D&D game in 1981. It came in a red box and featured the B2 Keep on the Borderlands module. It came with dice (and a marking crayon!). These rules handled levels 1-3. David "Zeb" Cook wrote the follow-on "Expert" rule book (another boxed set) that expanded the game to levels 4-14.
Frank Mentzer revised the game again in 1983 with another "red box" set featuring the art of Larry Elmore. This time, the Dungeon Master book was separated from the Player book. Mentzer would continue the Basic (1-3) and Expert (4-14) classifications but would go on to produce additional expansions: Companion (15-25), Master (26-36), and Immortal (characters too sexy for their levels, but you essentially get 36 more). These separate books would later be combined into the D&D Rules Cyclopedia.
Differences between Holmes and Moldvay
Moldvay made many changes to the Holmes version to streamline play and make it easier for players to understand the game. Both games cover levels 1-3, though.
Differences between Moldvay and Mentzer
In general, the Mentzer version was a repackaging and expansion of the Moldvay version. The differences are minor in the Basic ruleset.
Just adding to the excellent answers, it appears Holmes D&D was really more a continuation of OD&D than any sort of intro to the emerging Advanced Dungeons & Dragons. Holmes D&D is really almost a complete game in itself, separate from anything else ever published at TSR. Although continuations of Holmes' Blue book to higher levels can be found, Moldvay's version is really much more seamless in it's graduation to higher level play. To me that is the major difference between the two editions.
Moldvay's version in my experience is really a much better introduction into eventually playing AD&D, if you have the two books (Beginning and Expert) you have what is considered one of the most perfect contained RPGs ever published. The game Labyrinth Lord is based on the Moldvay version of D&D found in these two books.
The Mentzer version is the "Everything and the kitchen sink" approach....five box sets that take you from first level to, well, gods (immortals). I think this version was meant for the more "campaign" minded gamers who were immersed into the whole experience (gaining levels, setting up a kingdom, then becoming gods) than the first two versions, which seem to be more focused on low level and medium level play.
One stark difference between Moldvay and Holmes is that Holmes uses 1d6 for all weapons damage while Moldvay had each type of weapon roll different dice for damage.
All of them except Holmes use the simple stat mods; classic has the AD&D style mods in Supplement 1. All of them have variable weapon damage, some as an option; Classic, Moldvay, and Mentzer all have 1d6 damage for any weapon as standard. Alston and Denning use Variable Weapon Damage as a standard.
original or Classic D&D: levels 1-10+, Fighter, Mage, Cleric. All weapons do 1d6 hit points (at least one printing is missing that line). All hit dice in d6's with mods; completely reroll HP each level. Races are not classes.
Note: sometimes called "Little Brown Book" or "Little White Book" D&D.
CD&D with Supplement 1: add thief class and paladin sub-class of fighter, HD type by class and 1 HD per level, asymmetric stat bonuses tables (later used in AD&D), damage by weapon type instead of all doing 1d6, modifiers to to-hit rolls on weapon vs specific armor types...
CD&D Supplement 2: adds druids and assassins. Adds more stuff, too.
Holmes Basic: I don't have a copy; no details I can check. ISTR it used the supplement 1 stat effect tables.
Moldvay Basic: Introduces Race-based classes; Basic set levels 1-3, Fighter, Magic User, Cleric, Theif, Elf, Dwarf Halfling. Covers only dungeons.
Mentzer Basic: same classes and focus as Moldvay; different writing style, a few errata-ish changes.
Denning Basic: BIG black box (18x12x4 inches or so) Levels 1-5, 1st version without "All weapons do 1d6, but you have the option for polyhedrals," using only the damage by weapon type. Dungeon focused. Otherwise, very comparable to Moldvay or Mentzer editions.
Allston Cyclopedia: covers all the same as Mentzer through Master. Like Denning, no "1d6" option. Adds the General Skills from the Gazeteer and Hollow World series of modules.
Allston Wrath of the Immortals: complete rewrite of the immortals rules; works differently in many ways, includes a campaign adventure for both immortals and non-immortals (two sides of the same story!). Covers more details onthe multiverse and planes, covers levels I1 to I36, and on how to become immortal.
Advanced D&D just for clarity, Advanced D&D starts off with almost all of Supplements 1, 2, and 3 incorporated into the Player's Handbook and Dungeon Master's Guide. It uses the asymmetric stat modifier tables, variable damage by weapon, no racial classes, has Fighter, Cleric, Thief, Mage, Ranger, Paladin, Monk, Assassin and Druid, and a funky Bard class as well. It included the Supplement 3 psionics rules in an appendix, and was revised by Gygax from a base of Classic and Holmes.
Come on people...the dice!
Adam mentions that the Holmes version came with chits instead of dice after a while. When it came with chits, it also came with a coupon for a set of polyhedra. These were terrible, soft, twisted and awesome!
The white d20 would turn pretty spherical and roll forever after a year or so of play. The blue d12 was as soft as the others but it hardly ever got rolled, so they're the ones that we old-timers tend to still have around. ('Course, I still have all of them -- useless as they've become.) The green d8 seems like it was the second most used die -- it suffered the most damage after the 20. The red d6 -- my first one had this huge dent in one edge and it's still in pretty good shape. I think we maybe used dice from Yahtzee or something instead of the D&D die. And the yellow d4! Who could forget you? Ever leave this baby on the floor of the family room in the dark? Back then, no one had thought to flatten the points and they were like little caltrops.
By the time the red boxes came out, there were other, better, dice options in the glass cases of hobby and game stores and and TSR was shipping them with these little pastel dice. They were also soft plastic, but not as vulnerable as the originals, it seems. And they were littler than the originals and than the standard that has evolved. It seems like they were mostly blue, but maybe some beige or rose or something too. The set of dice in the box would be ALL THE SAME color though -- which was weird.