Let's discuss the ever-popular ellipsis versus the em-dash.

Ellipsis:

What you see in the title of this chapter is an example of an ellipsis. An ellipsis tells your reader to pause briefly. It's a gentle slowing of speech. Now, when I wrote my first novel and had an editor look at it I was told you must put spaces before and after the ellipsis, from my many google forays I've found this isn't necessarily true. It's more of a formatting preference. I personally prefer it, I think it looks nicer, space-wise. When you don't put the spaces before and after it looks too crowded together to me.  But again, it's a preference and you may find a publisher that prefers it differently than how you do it. 

An Ellipsis is also used to show when words are missing in the text. I'm sure you've seen this in quoted text before. It shows that there is more to a quote than what was printed. Generally the person leaves out items that aren't important to the actual body of the quote.

"It's a well-written book ... clearly on its way to becoming a classic"

Em-Dash:

The em-dash is a little tougher to explain. The easiest way to use an em-dash is to show when speech is cut off abruptly.  There are never spaces before or after an em-dash in books.  Newspapers, however, have been known to use spaces before and after them. 

  "Jonathan, please, what I meant was—" 

When someone interrupts a speaker and what they're saying is cut off abruptly, you would use an em-dash instead of an ellipsis, as when someone has a thought simply trail off. 

An em-dash is very versatile, it can be used to replace commas, parentheses, or colons. Each to a slightly different effect. 

Em-dashes in place of commas:

A pair of em dashes can be used in place of commas to enhance readability. Note that dashes are always more emphatic than commas.

Yet, when the car was finally delivered—nearly three months after it was ordered—she decided she no longer wanted it, leaving the dealer with an oddly equipped car that would be difficult to sell.

Em-dashes in place of parentheses

A pair of em dashes can replace a pair of parentheses. Dashes are considered less formal than parentheses; they are also more intrusive. If you want to draw attention to the parenthetical content, use dashes. If you want to include the parenthetical content more subtly, use parentheses.

Note that when dashes are used in place of parentheses, surrounding punctuation should be omitted. Compare the following examples.

Upon discovering the errors (all 124 of them), the publisher immediately recalled the books.

Upon discovering the errors—all 124 of them—the publisher immediately recalled the books.

When used in place of parentheses at the end of a sentence, only a single dash is used.

After three weeks on set, the cast was fed up with his direction (or, rather, lack of direction).

After three weeks on set, the cast was fed up with his direction—or, rather, lack of direction.

The em-dash in place of a colon

The em dash can be used in place of a colon when you want to emphasize the conclusion of your sentence. The dash is less formal than the colon.

After months of deliberation, the jurors reached a unanimous verdict—guilty.

The white sand, the warm water, the sparkling sun—this is what brought them to Hawaii.

En-dash:

There is also such a thing as an en-dash. Typically an en-dash is supposed to be used to show things like spans of numbers. 1999–2000 (not 1999-2010, that would be 1999 to 2010). Most people could care less about that pesky little en-dash and will use a hyphen. 

The en dash can also be used between words to represent conflict, connection, or direction. The Los Angeles–London flight. There is a north–south railway in the same area as the highway that runs east–west

An en-dash is only slightly wider than a hyphen, I suppose this is why most people don't bother using it. Why bother when most people have no clue what the thing is and probably won't even notice the difference?

I honestly had no idea what the thing was until I heard a few other authors debating its use one day.
So consider what it is you're trying to say and how you're trying to say it and then figure out where to go from there with your punctuation.