How do you count and categorize the different editions of D&D? I'm specifically talking about "official" (i.e. published by TSR or Wizards of the Coast) editions, rather than spin-offs, retroclones, and such.
Personally, I count 7 distinct editions (with sub-editions in parentheses):
-OD&D or 0E (Some might consider OD&D + Supplements to be "0.5E". Holmes Basic is hard to classify, but I sort of think of it as "0.75E" since it mostly seems to me like a clarified and abridged collection of OD&D rules, even if it was "intended" as a lead-in to AD&D or Basic D&D)
-Basic D&D...or, uh, "BE" or "BXE", I guess (I think of BECMI as "B.5E" and the Rules Cyclopedia as "B.75E")
-AD&D 1E (Some might consider AD&D + Unearthed Arcana to be "1.5E")
-AD&D 2E (I don't know enough about 2E to know if there's something that could be considered "2.5E", but I bet there is.)
-(A)D&D 3E (With 3.5E being a sub-edition and not a whole separate one on its own. If Pathfinder was an official D&D series published by Wizards of the Coast, it would probably be "3.75E".)
-(A)D&D 4E (With 4E Essentials perhaps serving as "4.5E".)
-D&D Next or (A)D&D 5E
So, to me, there are 7 versions of D&D that are different enough to be counted as "distinct," but I could see someone breaking things down much more particularly than that if they wanted to. For example, I don't see any point in considering 3.5 truly separate from 3E, but maybe some people would. If you wanted to get absolutely pedantic, you could even start splitting different printings of the "same" edition (e.g. the earliest and last printings of Holmes Basic) into different "editions" based on the smallest of fixes and changes, although I doubt anyone is really going to consider two extremely similar printings of the "same" book to be totally different editions or games or whatever.
I could also see someone grouping things much more loosely based on ease of conversion or other factors; OD&D, Basic, and 1E are all very compatible, and I think 2E is probably largely compatible as well, so you could argue that there wasn't a truly distinct, second edition of D&D until the "third" edition. You could say that pre-3E, 3E, 4E, and 5E are the only editions that are fundamentally different enough to be considered separate editions, or even separate games entirely.
So while I count 7 versions of D&D, I could see other people counting as few as 4 or as many as...geez, I don't even know. And of course, maybe none of this matters and it's all just hairsplitting, but I think that making some kind of distinctions could be useful (so players know what they're getting into when the DM says "Let's play Basic D&D," or "Let's play Fifth Edition,") as well as philosophically interesting to people like me who like to ask questions like "What is a game?" and "How many rules do you have to change before you are no longer playing the original game?" and "What separates a 'supplement' from an 'edition,' and what separates both of those from a different game?" If those kinds of questions bore you, that's fine, but I think the way we separate things, both linguistically and mentally, is pretty weird and confusing, and thus worthy of curiosity.
What do you think is the most useful and/or correct way to group or separate the various versions of D&D?