I’d like to say goodbye to “good-bye.”
The unhyphenated “goodbye” gets nearly five times as many Google hits. “Goodbye” is the preferred spelling in the Associated Press Stylebook. The American Heritage and Webster’s New World dictionaries list goodbye as the first spelling. Bryan Garner in “Garner’s Modern American Usage,” compares the hyphenated form to the archaic “to-day.”
Merriam-Webster, though, includes only “good-bye” and “good-by.” Many style guides, including the Chicago Manual of Style, prefer a Merriam-Webster dictionary, so “good-bye” is with us for now.
The word in any form is only a few hundred years old, stemming from the earlier “good morning” and “good day,” etc., and a shortening of the phrase “God be with you.”
Addendum (May 26, 2013):
Merriam-Webster’s newest dictionary, the Advanced Learner’s Dictionary, has no hyphens in its entry for “goodbye,” giving only the “goodby” variant. I would guess we’ll see the hyphen slip away in the new online Unabridged at some point soon.