In 1758 Charles Messier, a young French astronomer, was trying to find the comet which Edmond Halley had predicted would return in that year -- the comet we now know as Halley's Comet. While hunting for the comet he happened across a small fuzzy patch in Taurus which looked in a small telescope just like a comet, but did not move among the stars from night to night, as comets do. This fuzzy patch had already been discovered by John Bevis in 1731, but became most famous as M1, the first item in a list which Messier began to compile of faint fuzzy objects which might be mistaken for comets.
Messier eventually observed forty-four comets, of which thirteen were independent discoveries, and twelve carry his name in recognition of the discovery, so he was an exceptionally successful comet-hunter. Nowadays, however, what he is most remembered for is his list of faint fuzzy objects, the Messier Catalog. The objects on this list represent the majority of the easily observable dark-sky objects visible from northern latitudes, and include many of the most beautiful objects in the heavens.
Note: Messier's catalog only contained 103 objects. M104 through 110 were added to the catalog more than 200 years later, and M102, though probably more or less correctly identified, is still a matter of discussion more than 230 years after its supposed discovery.
Images of all Messier objects, including some added after Messier's death. (Wikimedia, Thierry Lombry)
(The image of M102 is not the same as elsewhere on this site, as its identification is uncertain.)