A preliminary note: I teach classes in the history and practice of navigation at Mystic Seaport Museum in Mystic, Connecticut, and in July I am teaching a weekend class in lunars. Details here: http://ReedNavigation.com. Also for broad discussions of all topics in celestial navigation and other forms of traditional position-finding, I highly recommend the message boards of the "NavList" community located at http://fer3.com/arc. There is no place on the internet that has hosted more discussions of lunars, longitude, and related topics.
A few of the comments here expressed disappointment that Harrison and his time-keepers weren't mentioned. They may have missed the point. The dominance of a specific choice for the Prime Meridian began with the lunar tables and NOT with the use or function of chronometers. Furthermore, lunars (or "lunar observations" or "longitude by lunar distances") were available almost immediately starting in the early 1760s when Maskelyne published his "British Mariners' Guide" and especially after the annual publication of the "Nautical Almanac and Astronomical Ephemeris" starting in 1767. That "Nautical Almanac", unlike its modern descendant with a similar name, was almost entirely devoted to finding longitude by lunars. And those longitudes, right from day one, were based on the meridian of the Royal Observatory in Greenwich. Chronometers, meanwhile, were rare and temperamental until the early 19th century. In 1802 when Edmund Blunt began publishing the first edition of Nathaniel Bowditch's famous "New American Practical Navigator", Bowditch wrote that chronometers could not be relied upon and in general they were quite rare at that time. He advocated lunars. Put it in historical perspective: chronometers were the original "black box" --mysterious machines that had to function perfectly with minimal interaction from users. Navigators only really began to trust chronometers decades later especially when ships began carrying three or even more chronometers which could serve as checks on each other.
The real proof of the significance of lunars exists in the mundane documents that fill libraries around the globe: ships' logbooks. Lunars were indeed widely used at sea from 1767 until about 1850 when they nearly disappear. That's over 75 years of active use of this method. It's worth noting that lunars faded into history much earlier in those parts of the maritime world where chronometers became common sooner. In the Royal Navy, for example, lunars were nearly over and done by about 1825 and they are only rarely encountered after that. It's also important to recognize that lunars were never used "just like" chronometers. Lunar observations were typically taken over the course of a few days right around First Quarter and Last Quarter phases of the Moon, when the Sun and Moon were conveniently "in distance". Between these fortnightly resets, the longitude was either determined by "dead reckoning" (before roughly 1835 on American commercial vessels) or in later years by a chronometer of uncertain reliability (up until about 1850 on American commercial vessels). Even on voyages where chronometers were available, it was common practice to observe lunars regularly, too, as a means of resetting the chronometer's error.
The "myth" of lunars is one of the flaws in Dava Sobel's otherwise terrific "Longitude". She intentionally paints Maskelyne as a villain and even says so. She mistakenly characterizes lunars as exceedingly difficult, which they were not at all after 1767 (though they did require an unusually good and well-adjusted sextant). These mis-characterizations of lunars and sputtering at Maskelyne are found in the era, too, by the "partisans" of the Harrison family. And it's important to recognize that they were indeed "partisans". Scathing attacks were published on both sides. Late 18th century Britain would remind many people today of the modern internet. "Posts" were made defending various points of view and attacking other points of view. Printed in pamphlets, they reached a much smaller community, of course, but the exchanges had the same dynamic that we see today in heated online exchanges. Unfortunately some modern commentators (and Sobel was hardly the first to make this mistake) do not understand this context. Harrison was by no means some innocent victim of the astronomers and mathematicians, pleasing as that image may be to some modern readers. Follow the money. He was amply rewarded long before the successful time-keeper known today as "H4". The awards from the Board of Longitude were princely sums in those days. In addition, Harrison received the Copley Prize, the greatest scientific honor in all of Britain in that era, long before the success of H4. Thanks to the huge commercial success of Sobel's "Longitude", Harrison's side of the story is now very well known. And let's be clear, lunars were eventually inferior to chronometers. There's no doubt about that. The Harrison partisans were right in the long-term, but it took 75 years for their case to be conclusively proven.
Finally, it's intriguing to note that "lunars" were shot by the Apollo astronauts, especially by Jim Lovell on Apollo 8. They served as a backup to ground-based tracking and rather than determining GMT or some other time variable, their purpose was to fix the spacecraft's position in space and correct the computer-managed "state vector". I presented a paper on "Lunars in the Space Age" at the "After Longitude" conference at the National Maritime Museum in Greenwich last year.