Original D&D, today you can buy Supplement I: Greyhawk (links now go to the new DM's Guild, which is replacing D&D Classics) and complicate things.
Categorically, Greyhawk is when OD&D began to be recognizably Dungeons & Dragons. High Strength made you hit harder and more often. High Dexterity improves your armor class. There were half-elves, thieves, and paladins. Swords do d8 damage and daggers do d4, as fighting-men went to d8 hit dice and magic-users to d4s. Magic Missile and Web and 7th through 9th level spells all got introduced in Greyhawk. Beholders and Owlbears and Bugbears all came to be in this supplement. It is whence the Deck of Many Things. In short, the things that made D&D a recognizable brand come from this booklet, to a degree that is surprising in retrospect.
That said, OD&D plus Greyhawk is not a particularly good combination for gaming in 2016. A few Greyhawk elements are worth grabbing, such as the thief (Zach Howard at the Zenopus Archives put together a good reference sheet for the pre-Greyhawk version). If you want to run a game with OD&D roots that is classically D&D, a better bet is using the Holmes Basic book with the Cook/Marsh Expert book (the two blue books); the result will be cleaner and better organized. Greyhawk follows OD&D's sections literally, meaning that information such as thief abilities are scattered across a dozen pages of unrelated content.
Greyhawk's problem isn't that its material is no good; it's that its approach has been taken much further. AD&D, classic D&D, and most of their derivatives all take the material here and do more with it. It's interesting as a historical artifact, but if your goal is to play OD&D, it works best as a snapshot of areas that could be expanded from the brown books.
It's interesting to see how much Greyhawk changed things. It touched on every aspect of the game, usually adding new layers of complexity. Ability scores, classes, races, combat system, spells, monsters, magic items - everything is added, and it becomes easy to see why it was named "Greyhawk" as the world is now much more Gary Gygax's. Once you have the idiosyncratic rules and creatures of the Greyhawk world, every setting starts to blend in with the next.
Once you remove that layer, OD&D's setting (which of course I've written about) becomes much more flexible. Each monster, spell, or magic item you choose to add does more to customize the game, because you're no longer fighting the now-entrenched Gygaxian assumptions. A beholder is interesting, but that's the kind of threat Gary's world features. OD&D has plenty of directions to go: there's Tolkienesque fantasy, classical mythology, Universal and Hammer films, '50s sci-fi/horror films, giant versions of normal animals, dinosaurs, Edgar Rice Burroughs's Barsoom, and several minor influences. Anything from fantasy, sci-fi, or horror is fair game, as are wholly new creations.
Empire of the Petal Throne is the furthest-reaching example of where this can go. A whole world constructed from the base up. But with OD&D as a basis, the referee doesn't need to create everything, and has a fairly stable basis for their variation. Using Greyhawk short-circuits this and leads back to the over-exploited, familiar soil.
I don't want this to be misconstrued. Greyhawk was where a number of classic ideas that have entertained people for decades got their origin, and deserves to be read as such. I just think that, as far as OD&D today goes, there is a sound creative reason to go back to the sources, and adding Greyhawk in is a distraction from that.