c. 1600, from William Shakespeare’s Hamlet, “to be or not to be.”
This is a pretty big one. Google returns 13 million plus hits for it, and snowclone.pl gives 700+ different variations on X, including rent, file, cut, drink, teach, speak, grow, herd, cheat, certify, etc etc. The X slot is very flexible (it’s mainly limited to the class of verbs, but nouns appear in it too), which helps put variants of this snowclone nearly on the order of “X is the new Y”. Literature critics, sports writers, and teenage bloggers alike may employ it, because who doesn’t want to demonstrate familiarity with the Bard?
Hamlet’s original utterance is morose and philosophical, of course. You can’t get much more emo than pondering suicide, considering whether not “to be.” Since X is so semantically flexible, however, modern variants do not recall this feeling of overwhelming responsibility. Of course, a user of the snowclone may wax philosophical on subject X, anyway, depending on how Shakespearean he’s feeling.
This snowclone has migrated to German, as well, as reported by Emmanuel Dammerer: “X oder nicht X” shows landroller (scooter) and auslaufen (to leave or run out) in the X slot. I noticed a lot more reference to “the question” (“To or not to be: that is the question. / Whether ’tis nobler in the mind to suffer the slings and arrows of outrageous fortune…”) in the German instances than the English ones, interestingly, though this may reflect something of the nature of snowclone.pl’s output (it’s hard to rely only on Google results because “or not to” is such a vague phrase) as much as actual usage.
Edited to add: This snowclone was covered back in October 2005 on Language Log. Arnold Zwicky points out something that I try to keep in mind when considering the instances in print, that a “to X or not (to X)” statement may be a natural contrastive disjunction, and not intended to echo Shakespeare. E.g., in a sentence like “To debride or not to debride is dependent on accurate assessment of the wound and patient condition”, a reference to the Bard is not meant, so though it looks like a snowclone, it isn’t really one.