http://dictionary.reference.com/browse/daemon Pronounces it DEE-mon which is how I've always said it. (The Golden Compass audiobooks and movie also pronounce their spirit animals, called Daemons, as DEE-mon).

I always thought the UNIX term came from the meaning of a subordinate/helper spirit (which is what they are, basically - helper services)

Edit: interchangeably, DEE-mon or DEE-mun