Currently, my daughter is reading Greco-Roman history, Greek myths, Bible stories, Lives of Saints, Aesop's fables, and American and British children's novels; she's learning French; she's playing and listening to Western European classical music on Western European classical instruments.
With home schooling you have the lattitude to include anything you want, and, in particular, to fill any gaps that your child would otherwise experience in the public education system. So why have we chosen such a Western, Eurocentric curriculum when we could be drawing from all over the world?
On closer inspection, our curriculum isn't as Eurocentric as it first appears. Our history source, for example, is The Story of the World. Before we got to the Greeks and Romans we spent time with the ancient civilizations of Egypt, the Middle East, China, India, and the Phoenicians. Later we encountered the Persians and the Carthaginians and, later still, Byzantium. I myself have learned more about early South America and early sub-Saharan Africa from The Story of the World than I have from any public school textbook. As for our classic tales, we'll soon be moving Eastwards to the Arabian Nights.
My daughter has moved eastwards in music as well. In addition to Bach and Beethoven, she is also playing Kabalevsky. The math she does is decidedly Singaporean. The animals she's learned about (our 4th and 5th grade home school science has been largly zoology) hail from all over the globe.
To be fair, though, most of the humanities topics we cover do fall into that much-maligned Western canon. So I'd better have good reasons for choosing this route. Stay tuned for Part II...