Since I am nearly completely incapable of finishing a sentence, I use the ellipsis VERY VERY often. Except right there, I didn't, I finished a sentence. OH, and did you see? I just did there, too! Anyway...
Wikipedia, the source of all knowledge says the following:
Ellipsis (plural ellipses; from the Greek: ἔλλειψις, élleipsis, "omission") is a mark or series of marks that usually indicate an intentional omission of a word in the original text. An ellipsis can also be used to indicate a pause in speech, an unfinished thought, or, at the end of a sentence, a trailing off into silence (aposiopesis) (apostrophe and ellipsis mixed). When placed at the end of a sentence, the ellipsis can also inspire a feeling of melancholy longing. The ellipsis calls for a slight pause in speech.
The most common form of an ellipsis is a row of three periods or full stops (...) or pre-composed triple-dot glyph (…). The usage of the em dash (—) can overlap the usage of the ellipsis.
The triple-dot punctuation mark is also called a suspension point, points of ellipsis, periods of ellipsis, or colloquially, dot-dot-dot.
But did you see that cool thing in the middle there, the "aposiopesis"? I didnt' know there was a word for when my characters talk like me! I'm telling you-- this has made my day. I decided that I was going to start learning a little more about grammar and punctuation, and here I learned TWO NEW THINGS IN ONE DAY! I am also a big fan of the em dash. I wonder if there are bumper stickers?