Wait, what about the case of a sentence ending with an acronym or abbreviation that uses periods? Or do no acronyms carry periods anymore? I can’t think of one offhand, so I’ll use S.W.A.T. as the example:
We need to call in S.W.A.T.
My recollection of proper grammar was that you would not put an extra dot at the end. So, the above is correct, whereas the following is wrong:
We need to call in S.W.A.T…
Wouldn’t the same logic apply to an ellipsis?
Cervaise has it perfectly, according to all known logic. But your employer (like mine) might disagree.
And you can generate this extended ASCII character by holding down the “Alt” key and striking 0133 on your number keypad … .
No. The final period in an acronym is treated exactly the same as any other period. So if you were excerpting your sentence from a larger paragraph, it would read:
We need to call in S.W.A.T…
Not to nitpick, but two hyphens (–) do not equal one emdash (—). 
Indeed. And an em dash is generally inserted with no leading or trailing spaces—thusly.
Well, Poly may have been typing on a keyboard that makes the emdash hard to access. I have no problem on the one I’m using here at work — it’s got its own number pad — but my laptop at home makes it a pain in the ass. Ya gotta hit function F9 to turn on the embedded number pad, type Alt-0151 to get the character, then hit function F9 again to turn off the number pad. So I’ll sometimes cheat with the double-hyphen, even though I know it’s “wrong.”
Which brings up a whole separate discussion: Are there degrees of “wrong-ness” in grammar? Isn’t the point of language communication? As long as somebody understands what you mean, isn’t everything else secondary? I was in a meeting yesterday where somebody answered a question by saying, “Her and I will be doing it.” The incorrect usage made me wince, like somebody had flicked my mental nutsack, but the meaning was perfectly clear; there was no ambiguity in interpretation.
Really, what we’re talking about here, I think, is that usage should be as clean as possible so there are no distractions to get in the way. It’s why I put spaces around my emdashes, even though as UncleBeer says it’s not standard, because I think it makes the text easier to read. And in the above example, when “her and I” floated across the table, I missed the next couple of sentences while the grating misuse bounced around my skull. “Correct” grammar, in my opinion, is best defended on the grounds that it doesn’t get in its own way, not on abstractly elitist “do it because it’s right” grounds. And this is applicable to the OP with respect to the “correct” use of ellipses because readers who “know better” will navigate the text awkwardly, like they’re riding a bicycle through an annoyingly potholed road, while readers who don’t know better won’t even notice, like they’re plowing a big car with spongy suspension over the same road.
That starts to turn into a IMHO or GD topic, though, regarding why it matters to get this stuff right; but I’d assert it’s worth it, if for no other reason than respect for the readers for whom this stuff matters, and leave it at that.
If I removed all of the distractions from my writing there wouldn’t be anything left. I write here like I speak, with as much of the snotty tone and campy emphasis intact within the limits of the software. But I agree that the REAL point of language is not hearing myself speak but to communicate and not only CAN the rules be evaded as long as you make your point but some SHOULD.
Grammar and syntax are critical in laws, treaties, contracts, and computer programs. Everywhere else you have to keep an open mind.
Pet peeve time. We are not talking about grammar here in any way, shape, or form. Grammar is an intrinsic property of the language.
What we are discussing is style. Style is merely a set of conventions for setting language down in typography (or, more rarely, handwriting or printing) so that it is still understandable. Capitalization, spelling, and text referencing are not part of the spoken language. There are no ellipses in speech. They occur only when trying to fix the language down on a page.
There are not and cannot be rights and wrongs when it comes to styles. There are merely accepted ways of handling situations so that the typographer hopes that as many readers as possible will understand the author’s meaning.
Many of the same issues of understanding come up when discussing grammar as well, but that’s a different, if allied subject.
Agreed, Exapno Mapcase. And as Cervaise also said, punctuation is aimed so the maximum readership understands it with the minimum of brainfreeze. So we’re not talking style either, properly, if I may nitpick your word choice; we’re talking about typographical tradition. Closely adhering to tradition insures that most of your readers will pass right by the punctuation without a blip, I think we agree. (Of course, typography says a full stop isn’t the same thing as a period, too, but we won’t go there.)
As for my own pet peeve, we’re not talking about “well, we use them this way in mathematics, so it makes sense that…” or “well, a computer uses ellipses in this manner, so logically…” or any other interpretation from the school of Well It Stands To Reason.
The last time I read my Strunk & White, it had the following to say:
A sentence that trails off unfinished ends with three periods. (Whether you put spaces between the periods or not is a matter of typography.)
An incomplete excerpt of the first part of a quotation may end with four periods to signify the missing material and the excerpt’s own final full stop, as: “Early to bed, early to rise, makes a man healthy … .” (Spaced apart for clarity.)
A pause in spoken dialogue, or skipped words in a quotation or excerpt, can be represented by an ellipsis of three periods.
But that’s Strunk & White. Other style manuals may say other things; ultimately, however you decide to punctuate, be internally consistent.
FISH
No, you may not nitpick my word choice. 
I said style, as in the topics covered by style manuals, as in the examples you used in your own post, as in the Chicago Manual of Style I quoted earlier on the subject of ellipses.
Styles may be traditional, but they in actual practice change frequently, which is why the 15th edition of the Chicago Manual recently appeared.
On the Commentary to Star Wars Episode 1 (The Phantom Menance, Lucas (or another person under him) commented on the fact that all Star Wars’ opening story (back story) will always have 4 dots in the Ellipsis. It seem to be implied by this that it was a rare thing, if not invented for this purpose in the first place.
Slight Hijack;
The first time I saw Naive spelled, I noticed it was with an umlaut over the i. Yet, the regular dot was not shown. Has anyone ever seen a i with three dots?
I gave up in the Bs while checking my fonts but I don’t recall seeing an i with three dots. There really isn’t room for the one without visual or actual smearing.
When a lowercase I is accented (I’m not sure an umlaut counts as an “accent,” but you know what I mean) in any way, the regular dot is dropped, whether in writing or in typing.
accent- í
grave accent- ì
umlaut- ï
circumflux accent- î
Please do … I’m intrigued! I always thought they were one and the same. 
Next thing I know, this post will be about gluttural stops and the schwa ə
I love this thread, and even though it’s nearly 10 years old I’m going to revive it. If there’s even a chance of anyone appreciating this, it’s you lot.
Fish is/was correct, as with the advent of Unicode we finally have the ability to provide separate glyphs for nearly everything, with no need to overload characters. And with advanced input systems, like Linux Compose, or the auto-substitution performed by systems like M$ Office and LibreOffice, we can readily access them. (No, I don’t consider typing out character codes with ALT+numberpad to be “ready access”.)
So, finally, we have ellipses… not merely series of periods. At least eight different widths to use for space characters. Real “open” and “close” quotes. Over half a dozen dashes, to supplement the hyphen — not just em and en, but figure, swung, quotation, two-em, and three-em. And, of course, combining glyphs that facilitate s̶o̶m̶e̶ ̶f̶u̶n̶ ̶t̶r̶i̶c̶k̶s̶ even more advanced typography.
Which is why I find it interesting what’s not provided in Unicode. Consider:
[ul]
[li]From the Unicode perspective, a period (U+002E) is a full stop (is a decimal point).[/li][li]The right-single-quote and the apostrophe are one and the same. There is no separate apostrophe character. The ASCII character ’ is the apostrophe-quote (U+0027), but that glyph includes the following notes:[/li][LIST][li] U+2019 RIGHT SINGLE QUOTATION MARK is preferred for apostrophe[/li][li]preferred characters in English for paired quotation marks are U+2018 LEFT SINGLE QUOTATION MARK & U+2019 RIGHT SINGLE QUOTATION MARK[/li][/ul][/LIST]
Though, in the case of the period, there is also the separate U+3002 IDEOGRAPHIC FULL STOP。
Why do you know any of that?
Because he’s a nerd. Is any further reason necessary?