"Between 1960 and 1975, European film production companies made nearly 600 Westerns. Critics either blasted or ignored these films, and because most of them were financed by Italian companies, they called them Spaghetti Westerns. Fans of the genre embraced the term which is now lovingly used to label any Western made and financed by Continental filmmakers."
- John Nudge, ImagesJournal.com, Issue 6
In my experience, however, the term refers to three specific spaghetti westerns, directed by Sergio Leone, which marked a turning point for westerns:
It's actually difficult to overstate the impact of these three films on the genre. Up until that point, the "western" had been a uniquely American genre - what could be more American than a western? Unfortunately, decades of Hollywood westerns had built up the "Myth of the American West" to the point that its icons, gramar, and stereotypes had become completely entrenched. While a few westerns of the 1950's had begun to deconstruct parts of the myth (see "High Noon" (1952) with its cowardly townfolk and "The Searchers" (1956) with its vengeful protagonist), they still retained their inate sense of right and wrong. There were moderately successful westerns produced in Europe before "A Fistful of Dollars", but they were only imitations of B-movie westerns from America.
"Get three coffins ready."
The trilogy mentioned above used the western setting, but removed or distorted other key elements of the western genre. They portrayed a west which had lost any sense of "pioneer spirit", where life had become cheap and death even cheaper. This west was a culture breathing it's last gasps with the jackals drawing near and buzzards circling overhead. A deadly merciless sun baked the landscape, and a layer of grit covered everything and everyone like grave dust. Also unlike previous westerns, that grit seemed to pervade the characters as well - no one was innocent or good, only more or less tainted.
That moral ambiguity even extended to the most sacred icon of the western: the protagonist, "the good guy". The nameless gunslinger, played by Clint Eastwood, was vicious, smart-assed, nihilistic, and so amoral he would have been a villain in a classic western. He remained ambiguous through all three movies, to the point we never even learned his name: he was only given the nickname of "Blondie" in the third movie, in the previous two all he got were variations on "Hey, Mister!” Yet, in part because of his inscrutability (and his snappy one-liners), audiences took an instant liking to him - the movies were soon known as "The Man with No Name Trilogy".
Like their protagonist, the trilogy had a style unlike any western made in Hollywood. Their cinematography, editing, and music remain fresh and recognizable to this day. The washed out colors, fast zooms, and tight close-ups of flinty stares shot by cameraman Massimo Dallamano were experimental for their time, but have become standard for most westerns since. The editing varied tempo to match the sparse, tense music. Speaking of music, Ennio Morricone's theme from "The Good, the Bad and the Ugly" is one of the most recognizable clips in the world, and has become synonymous with westerns and high-noon showdowns.
"I'm faster than you'll ever live to be!"
This trilogy revitalized the western genre by freeing it from itself. Spaghetti westerns remained popular and often interesting for years after, some of the more notable being "Django" (1966), "The Big Gundown" (1966), and "They Call Me Trinity" (1970). For Hollywood in particular, the next few years produced some of the best known westerns ever, including "Hang 'Em High" (1968), "Once Upon a Time in the West" (1968) (also directed by Leone), "The Wild Bunch" (1969), "Butch Cassidy and the Sundance Kid" (1969), and "High Plains Drifter" (1972) (a remake of "Django the Bastard" (1969), dedicated to Leone and Don Siegel). Every one of these shows signs of the influence of these three spaghetti westerns, as do most westerns and many other movies since.
Sources:
http://www.imdb.com/
http://www.turnerclassicmovies.com/
http://www.imagesjournal.com/issue06/infocus/spaghetti.htm
Thanks to wertperch for being so patient with all my questions and sid being so cool.