Earlier today, as we were looking at the warnings of the impending White Doom from Above, I was asked to weigh in on the northeaster/nor'easter issue.
Both terms refer to a storm with northeast winds. Merriam-Webster's Unabridged lists only the first spelling, tracing it to 1753. The Oxford English Dictionary has a 1753 citation from the Boston Post-boy for northeaster and an 1837 citation for nor'easter from a translation of Aristophanes' Knights.
So both have pedigree, which leaves us in the treacherous situation of basing a judgment on social, cultural, or regional factors.
My suspicion is that nor'easter is a colloquial shortening of the original word, which is borne out by some of the evidence, such as the OED's citation from A.J. Cronin's Hatter's Castle (1931): "Did you see that shot of mine, cocky?.. It was a—a regular nor'easter—a pickled ripsnorter."
And I have heard someone sneer at the use of nor'easter as a ludicrous faux-Yankee affectation, the impression being that you have no business using it unless you are outfitted by L.L. Bean, speak with a broad a, and typically respond to people with a laconic "Eh-yuh."
At The Sun, with my slack hand on the tiller, we have allowed both northeaster and nor'easter into print, and neither the paper nor the English language has collapsed. So use whichever form seems to be appropriate for the occasion and your audience. If you're not Down East yourself, you might find northeaster marginally safer.