You can use it for omission or hesitation, but is it too annoying?
The Comic Strip Ellipsis
I wouldn't consider this formal writing, but comic strip writers have been known to use ellipses instead of periods. I'm speculating here, but it seems as if the ellipses are being used as a way to draw you into the next frame—as if they are saying, “Keep going; there's more to come.” For example, Charles Schulz always used ellipses instead of periods at the end of sentences in Peanuts.
The Gossip and Show Business Column Ellipsis
Next, I was surprised to see that The Associated Press Stylebook allows the use of ellipses for what they call “special effects”: The stylebook states, “Ellipses also may be used to separate individual items within a paragraph of show business gossip or similar material.”
Some famous newspaper writers have used ellipses in this way instead of periods to separate their rambling thoughts. Larry King heartily used ellipses in his USA Today column, as did Herb Caen in his San Francisco Chronicle column. In fact, Herb Caen is reported to have coined the phrase “three-dot journalism” to describe such writing, and he was so beloved in San Francisco that when he died the city named a street after him—and included an ellipsis in the name: Herb Caen Way . . . (5).
To sum up, use ellipses sparingly to indicate hesitation or faltering speech or thoughts, and use them to shorten long quotations when necessary, but be sure you don’t change the meaning.
Web Bonus: How to Make an Ellipsis
Now that you know how to use ellipses, you need to know how to make them. An ellipsis consists of exactly three dots called ellipsis points—never two dots, never four dots—just three dots.