Hesiod: Volume 1, Theogeny. Works and Days: Testimonia. Hesiod. New York: Loeb Classical Library, 2007.
Zeus: King of the Gods is unusual for this series because it takes the bulk of its inspiration from one source myth, Hesiod's Theogeny, with a few little bits from other old myths sprinkled here and there. The above is the copy I have in my personal collection; it was the best translation I found.
Theoi Greek Mythology Website
Without a doubt, the single most valuable resource I came across in this entire venture. At theoi.com, you can find an encyclopedia of various gods and goddesses from Greek mythology, cross referenced with every mention of them they could find in literally hundreds of ancient Greek and Roman texts.
A subsection of the above site, it's an online archive of hundreds of ancient Greek and Roman texts. Many of these have never been published in the traditional sense, and many are just fragments recovered from ancient papyrus, or recovered text from other authors' quotations of lost epics. Invaluable.
Metamorphoses. Ovid. New York: Penguin Classics, 2004.
An excellent translation. Although Ovid was actually Roman (and Athena goes by her Roman name Minerva here), his is the only account we have of the story of Arachne (though the story does appear to be pictured on some Greek vases).
Myth Index Website
It seems this website is connected in some way to theoi.com, and is still being updated, which is nice. While it doesn't have the painstakingly compiled quotations of ancient texts, it does offer some terrific encyclopedic entries of virtually every character to ever pass through a Greek myth. Pretty amazing.
For younger readers
The Gods and Goddesses of Olympus. Aliki. New York: HarperCollins, 1997.
D'Aulaires' Book of Greek Myths. Ingri and Edgar Parin D'Aulaire. New York: Doubleday, 1962.
Black Ships Before Troy. Rosemary Sutcliff and Alan Lee. London: Francis Lincoln, 2005.
Wanderings of Odysseus. Rosemary Sutcliff and Alan Lee. London: Francis Lincoln, 2005.
We Goddesses: Athena, Aphrodite, Hera. Doris Orgel, illustrated by Marilee Heyer. New York: DK Publishing, 1999.
Z is for Zeus: A Greek Mythology Alphabet. Helen L. Wilbur and Victor Juhasz. Chelsea MI: Sleeping Bear Press, 2008.
For older readers
Athena: A Biography. Lee Hall. Reading MA: Perseus Publishing, 1997.
The Marriage of Cadmus and Harmony. Robert Calasso. New York: Knopf, 1993.
Mythology. Edith Hamilton. Madison WI: Demco, 1999.
Zeus: A Journey Through Greece in the Footsteps of a God. Tom Stone. New York: Bloomsbury USA, 2008.