My question is: Why not just use the perfectly serviceable alternative, “accidentally?” 
Oh… so because “e-mail” wasn’t in the dictionary until a couple years ago, any use of the term before then was “wrong”?
Looks like a linguist’s hat to me. Dictionaries do not dictate usage; they reflect it. If a certain word or construction is not used often enough, it doesn’t make it into the dictionary, but that doesn’t necessarily make it universally “incorrect”. For instance, “ain’t” may be considered incorrect for my dialect simply because the word is never (non-facetiously) used, but one could hardly dispute that the word does exist in other English dialects and that therefore it is, generally speaking, a “correct” English word. Dialects that use “ain’t” do have a strict set of grammatical rules governing when and where it may be used, and there is a specific meaning attached to the term.
Indeed. That syntax is more of a convenience than a necessity for the unambiguous conveyance of ideas was discussed by Landauer et al. in their paper, “How well can passage meaning be derived without using word order?” which appeared in the proceedings of the 19th Annual Conference of the Cognitive Science Society. They presented a cognitive model which gave compelling evidence that, even in largely non-inflected languages such as English, word order contributes surprisingly little to semantics. If you’re interested, a pre-print of the paper is available online at http://lsa.colorado.edu/papers/cogsci97.pdf.
I vote for it being a regionalism.
Most people I’ve met using the form were in the region of four years old.
Technically for me wearing my editor’s hat yes. I don’t deal with language like a linguist. For me, my bibles are the AGPS Style Manual and the Macquarie dictionary.
Practically speaking, a new word such as e-mail would be one that I would check with the publishing house and the author for the correct spelling and usage. By accident or on accident are not new words or expressions – if an author used ‘on accident’ in a m/s I’d either query it or correct it. It’s unlikely I would accept it unless it were in direct speech with a regional flavour.
I’m not a linguist, I don’t pretend to be a linguist and I work differently with words. That doesn’t make me wrong ;).
Well, if you’re speaking as an editor of English-language publications intended for a broad North American audience, then of course you’re absolutely right that “on accident” is incorrect. But this just reinforces my point that you can’t say whether a particular construction is right or wrong unless you take the context into account. Tedrlord’s friend was probably correct in saying he did something “on accident” since he was using what is presumably a regionalism or idiodialecticism in an informal setting where it was unambiguously interpreted. He didn’t have an editor standing behind his back, waiting to whack him over the head with her copy Fowler’s Modern English Usage for every dialect-specific utterance. 
No. I’m not editing for a North American audience (hint this is a global messageboard).
I’m getting irked with your approach it is somehow wrong to say that grammatically speaking ‘on accident’ is not strictly correct because it is a regionalism. Simply being a regionalism does not make it correct. I think we have established that ‘on accident’ is a regionalism and that context does matter. I certainly have not said anything different once it was established that it is a regionalism (it’s not a regionalism where I live, I’ve never heard it.)
And FWIW Fowler has nothing to say about it. I checked. Likewise Hudson, Strunk and White, Kane, Gowers, Peters and the six dictionaries I checked. I am beginning to wonder whether I should just chuck aside the bibles of my trade and accept any old pudder on the grounds that somewhere it might be a regionalism ;).
I have never heard the phrase “on accident” before. Could someone tell me who uses it? Is it a regional thing? What region? Is it limited to people of a certain age? What age? Is it more typical of a certain social class or race or sex or some such? Was it coined just recently? Was it spread by being used on a TV show or something similar?
From my humble standpoint saying “on accident” in any context sounds horrible. It’s just the incorrect preposition, and that bugs me. It really makes people sound less intelligent to me. Not fair, but I guess I am a bit of a grammar fiend.
On another note, I hate to nitpick (or maybe I love to. who can tell?) matt_mcl but it’s not as complex as the literal context you speak of. I’m not qualified to comment on Esperanto, but in Spanish at least the literal translation from the expression “para veinte dolares” as a matter of fact is “for $20.” Suffice it to say that prepositions are a lot more context sensitive than in English. Para can mean “by” “for” or “to,” depending upon context. Basically what I mean to say is that the discussion is not so meaningless as you say. To give a parallel example: If you were to say “por $20” in Spanish (“por” is used like English “for” in virtually all contexts) a native would know what you meant. However, you would be wrong, and would probably look pretty ignorant. That’s my take on the “on accident” thing. At least in Spanish, a native English speaker would have more of an excuse - getting those prepositions correct is quite a challenge for the beginner. In English though? Sorry bub.
Grelby writes:
> From my humble standpoint saying “on accident” in any
> context sounds horrible.
It sounds horrible to me too, but given this thread it must sound O.K. to somebody. Could someone who uses or has at least heard the phrase before tell us what region or age group or sex or race or social class or whatever it is used in?