|Sign of the Apache Web Server|
There exist two words in English which are spelled "Apache"; one is of French origin, and according to dictionary.com it means "a Parisian gangster, rowdy, or ruffian". This one does end in a silent "e", but it is not the one that the Apache Software Foundation was named after. The other word is of Mexican-Spanish origin, it means "a member of an Athabaskan people of the southwestern U.S.", it ends in a definitely non-silent "e", and it is the word you are looking for.
Head over to dictionary.com to check out these two words and click on the little speaker icons to hear their pronunciation: http://dictionary.reference.com/browse/apache
Also, in the Wikipedia article about the Apache Software Foundation (http://en.wikipedia.org/wiki/Apache_Software_Foundation) we read:
The name 'Apache' was chosen from respect for the Native American Apache Nation, well known for their superior skills in warfare strategy and their inexhaustible endurance. It also makes a pun on "a patchy web server"—a server made from a series of patches—but this was not its origin.And as a side note to fellow USAians: The same applies to the world famous Porsche brand of cars: the final "e" is not silent. Please quit saying porsh; it is por-sheh. See: http://youtu.be/4OuPY-1snyw