7th, I think:
1) OD&D
2) B/X D&D
3) BECMI D&D (later reissued as the "Black Box" and "Rules Cyclopedia", but these are just a repackaging of the same info, not a true new version)
4) AD&D 1st Edition * (post "Unearthed Arcana" and the two "Survival Guides" might or might not be considered a 1.5 Edition)
5) AD&D 2nd Edition ("Player's Option" may or may not be considered a 2.5 Edition)
6) D&D 3e (later revised as 3.5e)
7) D&D 4e (later revised as Essentials)
* I've placed 1st Ed 4th on my list, but that's an arbitrary choice; #2/#3 and #4/#5 were parallel developments.
In some ways, it's a shame that WotC decided to declare that 6th version to be "Third Edition". Still, given that they did so, and we've since had a decade of speaking of 3e and later 4e, it makes sense that the next version would be 5e.
You're leaving out at least one distinct iteration, 1977's Holmes Basic. And there are enough differences between the Mentzer and Denning/Allston versions that they are considered separate versions by most old-school enthusiasts. (Otherwise, you would have to lump B/X in there with BECMI. That's roughly the level of tweaks involved.)
The original D&D game-line has five "versions" or "editions":
1974 - Gygax/Arneson D&D, the white box plus supplements
1977 - Holmes Basic D&D, the blue box, goes up to 3rd level; it's quite funky and unique
1981 - Moldvay/Cook B/X D&D, the magenta and cyan boxes, up to 14th level
1983 - Mentzer BECMI D&D, the classic colored boxes up through Immortals
1991 - Denning/Allston D&D, the black box/Rules Cyclopedia/Wrath of the Immortals
Then you have the AD&D game, reportedly inspired by a combination of OD&D's incompleteness and opacity, and Gary Gygax's personal distaste for regional variants and individual DMs' house rules:
1978 ~ 1st edition
1989 - 2nd edition
2000 - 3rd edition
2003 - revised 3rd edition (labeled as a revision, but about as different from 3rd as 2nd was from 1st, so it probably counts for our purposes here).
2008 - 4th edition (maybe it's just me, but I can't see Essentials as being a separate version from 4th here, since it's extra stuff, not replacement stuff)
So if you were really to count discreet versions of the game, chronologically, and if you define "edition" as "new books that TSR/WotC expects to you buy to replace your old books", then you'd have:
D&D '74
D&D '77
AD&D 1st
D&D '81
D&D '83
AD&D 2nd
D&D '91
D&D 3rd
D&D 3rd-and-a-half (ugh, I hate calling it "point-five", it's so fugly...)
D&D 4th
Making "D&D Next" actually "D&D Eleven"!!!
