“...”

It's called an "ellipsis" (plural: "ellipses"), and it's used when there is a pause or when words have been left out of a sentence. It is also used in the place of words left out of a direct quote.

Examples of the first use:
"I don't know . . . maybe it isn't such a good idea."
"I know that bright colors are fashionable these days, but that dress. . . ."
"So, if you multiply 1/4 by 3/8, the answer is. . . ?"

Second use (quotation):
"I pledge allegiance to the flag of . . . America . . ." (Pledge of Allegiance)
"one nation . . . indivisible, with liberty and justice. . . ."
"What are these things called. . . ?"

Spacing rules:
If used inside a sentence, space between each period and on either side of the ellipsis.
If used at the beginning of a sentence and the excerpt begins with a lower case letter, an ellipsis is not used. But if the excerpt begins with an upper-case letter, it might be confused with the beginning of a sentence, so the ellipsis is used.
If used at the end of a sentence, the ending punctuation is retained and the ellipsis is closed up against the last word of the excerpt.

Never use an ellipsis where a colon should be used. It also isn't necessary to use the ellipsis if it's obvious that you're using just a couple words taken from a sentence (for example, if I was to quote "do you and do you not" from your question).

OK, so much for the goody-two-shoes rules.... Online, it's easier and looks better to violate all the rules and just follow your statement by three or four closed-up periods, depending on whether or not you are at the end of the sentence. If you don't close up the periods, HTML will do it for you.