Kozijat rog (1972), released in the US as "The Goat Horn" was directed by Metodi Andonov. It is set in 18th century Bulgaria and is a tale of revenge. One reviewer on the excellent IMDB website described it as "an excellent movie, the Bulgarian equivalent to an Italian neo-realism masterpiece. The degree of freedom to artistic expression is extra-ordinary, especially if replaced into the context of the political environment prevailing in Bulgaria in the 70s."
I once got drunk in Bulgaria in the late Seventies on a single tot of gin. I had to lie down. I don't think it was a pure spirit.
Anyway, spurred on by this (and the update in particular), I can reveal that IMDB lists no fewer than 71 movies with 'goat' in the tile, admittedly including short films and documentaries. The first is a silent movie called "Goat" released in 1887. The most recent is "Goat" to be released in 2006, directed by David Gordon Green and based on a memoir by Brad Land about a frat house hazing incident at a US college.
Among the remaining titles that catch the eye are:
A Buster Keaton short, "The Goat" (1921);
Goat on Fire and Smiling Fish (1999) aka "Smiling Fish & Goat On Fire" (USA);
La Chèvre, La (1981) aka "The Goat", starring Gerard Depardieu and Pierre Richard;
Ballada o kozie (2004) aka "Goat Walker", in Polish;
The Hungry Goat (1943);
Hogan's Goat (1971) (TV) which has Fay Dunaway;
Urusei Yatsura: Yagi-san to Chiizu (1989) (V) aka "Urusei Yatsura: Goat and Cheese";
Getting Andy's Goat (1914);
Getting Buster's Goat (1929);
Getting Father's Goat (1915);
Getting Gertie's Goat (1924);
Getting the Gardener's Goat (1915);
Goat Getter (1925);
The Goat Girl from Bear Canyon (1912);
Goofy Goat Antics (1933);
Handy Mandy's Goat (1920);
Mighty Lak a Goat (1942);
Tertern u aytze (1941) aka "The Priest and the Goat";
Felix the Goat Getter (1923);
and Fiesta del chivo, La (2005) aka "The Feast of the Goat", based on the novel by Mario Vargas Llosa.
While not in the actual title, there is a controversial shot of a goat falling to its death in Luis Buñuel's Las Hurdes: land without bread (Spain, 1932).
That's not all. There are memorable goat references in several films, including:
Automated voice: You have reached Ritual Sacrifice. For goats, please press "1" or say "goats". To sacrifice a loved one or pet, press the pound key.
Dave the Barbarian (2004)
Candy: Ooh, the new goats are in.
Rolling Kansas (2003)
Dick Murphy: I hate goats. They're weird.
A man goes to the movies, buys his ticket and takes his seat. He notices that his neighbour to his left looks and smells like a goat. He turns to the neighbour and says, "Excuse me, are you a goat?"
"Yes," replies the goat.
"What are you doing at the movies?"
"Well, I liked the book."