Of course, it is a little silly and possibly self-contradictory, since knowing one thing means knowing something, while knowing nothing precludes knowing something.
Still, if Socrates said it, it's worth repeating, right? (For kicks, Google it and see how many times it is quoted authoritatively.)
But I wonder if Socrates ever said it at all.
Yes, I know that we don't know exactly what Socrates said. Socrates left us no writings, and as for transcriptions of his conversations, we have only three first-hand sources to rely on: those of Plato and Xenophon his students, and of Aristophanes his ostensible rival. It seems likely that Aristophanes did not attempt to represent Socrates accurately, nor as a philosopher. Plato may well have invented much of Socrates' dialogue as well, but he also had a stake in continuing and defending the philosophical work of Socrates in Athens.
For this reason, when philosophers refer to Socrates, we are usually referring to the Socrates found in Plato's rather extensive writings.
So did Plato's Socrates ever say "en oida oti ouden oida"? It appears not.
The closest thing I've found is a passage in Plato's Apology of Socrates, where Socrates says something that should really be translated as something like this: I do not claim to know those things that I do not know.
This is not only more reasonable, it's also good advice: don't pretend to know what you don't know and you'll avoid a lot of trouble.
It's important for another reason, though. The "en oida oti ouden oida" quote seems to be something of a staple of frosh philosophy texts and classes.
The danger here is that we will present an ancient philosopher (two of them, in this case) as though he were fairly foolish; and as a result, we will not take ancient philosophy seriously.
All it should take to cure this is a quick look at the Greek text of any of Plato's dialogues. The Phaedo, for instance, bears a slow and careful read in Greek, since no translation I've found captures all the wordplay. And as Peirce pointed out, when one reads the Greek, one discovers something else that the translators often veil from our sight: Plato's Socrates uses the language of syllogism in a way that shows that he was doing Aristotelian logic before Aristotle was.
By relying on hearsay rather than on engagement with the primary texts, we close off a path of inquiry into a whole set of ancient philosophical texts. "Doesn't their being ancient mean that they are exhausted?" you may ask. Old trees, it seems to me, may still bear rich fruit. And just as we find that old caves sometimes have rich troves of ancient unread texts, what else might we find if we take the time to read the ancients closely?