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I have heard conflicting accounts of the word "theory". One account asserts that the "theo" is related to the Greek word for god, and that theory originally referred to the reports made by an observer of Greek religious rites. Another account that I've heard suggests that the word does refer to observing, but is not related to the Greek word for god. I would appreciate any informed comments on this. Thanks very much.

From the Online Etymology Dictionary:

theory
1592, "conception, mental scheme," from L.L. theoria (Jerome), from Gk. theoria "contemplation, speculation, a looking at, things looked at," from theorein "to consider, speculate, look at," from theoros "spectator," from thea "a view" + horan "to see." Sense of "principles or methods of a science or art (rather than its practice)" is first recorded 1613. That of "an explanation based on observation and reasoning" is from 1638. The verb theorize is recorded from 1638.

This seems to confirm your second acount, that of observation without referring to a god.

On the other hand, also from the OED:

theosophy
1642 (implied in theosophical), "knowledge about God and nature obtained through mystical study," from M.L. theosophia (c.880), from Late Gk. theosophia (c.500, Pseudo-Dionysus) "wisdom concerning God or things divine," from Gk. theosophos "one wise about God," from theos "god" (see Thea) + sophos "wise, learned." Taken as the name of a modern philosophical system (sometimes called Esoteric Buddhism), founded in New York 1875 as "Theosophical Society" by Madame Blavatsky and others, which combines teachings of Hinduism and Buddhism.

And finally:

Thea
fem. proper name, from Gk. thea "goddess," fem. equivalent of theos "god," from PIE base *dhes-, root of words applied to various religious concepts, e.g. L. feriae "holidays," festus "festive," fanum "temple."

This seems to lead us in a circle! What's the relationship between thea meaning view and thea meaning goddess?

Looking at a Greek dictionary at the Perseus Project it appears that there at two different words spelled the same: thea from the feminine of theos meaning "goddess" and thea from the verb theaomai meaning "to look on, gaze at, view, behold."

Indeed, my trusty online translation page, Systranet, translates ΘΕΟΣ (THEOS) and ΘΕΑ (THEA) as GOD and VIEW, respectively.

(Note: I have never studied Greek (other than the Greek Alphabet for physics and chemistry), only Latin and French, so there may be more to this. I've found that etymology is like peeling an onion: there are sometimes many layers that can make you cry. )

Three years have passed since this post but the Feb 1 2011 Good Word on "Theory" was not posted on the Alpha Agora by the time that the next day's word appeared so one has to wonder why. I have trouble seeing why Dr. Goodword would post anything on a word starting with 'theo' without mention of the 'god' connection even if he believes the two words are totally unrelated.

Aimeusdietger, have a look at Dr. Goodword's article on historical linguistics
http://www.alphadictionary.com/articles/ling007.html
It explains how most of the western European languages (and several of those in the Indian subcontinent) developed out of Proto-Indo-European and how various empires and invasions have shaped modern English.

Reviewing this ancient text, I note that no one juxtaposed thea with theater, which obviously relates to viewing more than to God or gods, though deus ex machina was popular in some ancient plays as well as in todays pyrotechnics.

PS, almost forgot. "Theory" often becomes an oxymoron in today's debates between science and religion. They more conservative religious people use theory as equivalent to an idea that is speculative, what a scientist is more likely to term a hypothesis to be proven or disproven. A theory in science is a more established fact, although always subject to reappraisal as more evidence comes in.