About a hundred Web sites or more say oregano comes from Greek oros 'mountain' + ganos 'joy'. But I tell sneff "No, that looks wrong to me", then I learn about the hundred Web sites, do some research of my own, and say, "No, all those Web sites are wrong, definitely. To confirm this I'd better ask Gone Jackal and look up the OED, but I'm right, trust me." - So sneff obligingly puts <strike> tags through the official etymology. It's nice to be trusted in one's expertise but I think I'd better justify myself here. :-)

All those Web sites are herb or herbalism sites. They all copy the received etymology. Just multiplying it across the Web doesn't, unfortunately, make it stronger evidence. (Bear this in mind when researching nodes.) I turned to language sites and drew a blank. None of the sites (or books) I would rely on confirmed this etymology.

The standard lexicon of Ancient Greek is Liddell & Scott (Liddell was Alice in Wonderland's father), of which a modern edition is available on-line at http://www.perseus.tufts.edu/cgi-bin/resolveform. This captures more or less every form found in ancient texts. Put orig in the search field and it comes up with lots of grammatical forms of ori_ga^n-, with varying endings, but the crucial thing they all have in common is that long vowel i_ where long is indicated by an underscore. That was the Ancient Greek. That cannot have comes from oros + ganos.

For confirmation I asked Gone Jackal, who is far more expert on this than me, and got this answer:

no. in short; a 2nd declension )/oros, mountain, in a compound would demand either an -o- or long -a-/-e- (eta); an -i- is permissible as the ending of the initial element of a compound only when it is the natural stem-vowel of a 3rd declension noun. Either way, it would be a short vowel, even if the accent recedes back to that syllable. if you don't believe me, or want to check yourself later, this is from Smyth's Greek Grammar, paragraphs 872-873
What that says is that the compound would have been orogan- if it had come from oros. And even if oros had been of a grammatically different class, say oris, it would have given origan- with a short i, not the actual attested ori_gan- with a long i.

(An alternative writing of it was oreigan-, also with a long vowel: by the Roman period ei was pronounced the same as long i.)

The Greek word was borrowed into Latin as orîganum, also with a long i. (Vowel length is usually abundantly clear from metre in poetry, even though it was not normally written.) At some point it acquired a variant with a short i. The older English forms organy, organum and the Spanish oregano all come from a word with a short i.

The OED says oríganon, -os is "in appearance, a compound of 'ορος mountain + γανος brightness, joy, pride, whence the scribal alteration ορειγανος". For one awful moment I thought the OED might be wrong*, then I noticed the crucial expression "in appearance": yes, it looks like it does, so ancient commentators might well have constructed this very plausible folk etymology; but the OED and I, and you, know that it could not really be.

One other dictionary I consulted suggested an "African" word as the origin. Greek borrowed lots and lots of words, particularly cultural words like this, from neighbouring or substrate non-Indo-European languages. I have no idea what it does come from, just that it's not the compound that all those Web sites say it is.

Isn't that interesting?

Although this illustrates the perils of relying on sheer presence on the Web for information, perhaps I should emphasize that all those herbal sites were quite justified in repeating the etymology. They had good grounds for believing it to be true: I mean no criticism. In this case it is perhaps more like the scientific discovery of new information invalidating the old, rather than propagation of bad rumours.

* No, don't be silly. Think I might be wrong? Never.

By the way, this hasn't been mentioned: the usual British pronunciation is orr-i-GAH-no (orr- short as in sorry), the American o-REG-a-no. The difference is unrelated to the above.