Semicolons indicates a dramatic pause, which is later finished.
"This is not a good idea; it will lead us into danger."
"Hush!"
Ellipses (the dot-dot-dot thing) indicate a trailing off.
"I don't think that's a good idea..."
"Hush!"
Dashes indicate an abrupt cutting off.
"I don't think --"
"Hush!"
What's the difference between the dash and the ellipsis? With dashes, you cut off the sentence before it is complete. With an ellipsis, you indicate a cliffhanger sentence. It's still complete grammatically, but the idea isn't.
Ellipses and dashes are most effectively used in dialogue or first-person narration, although they can be used sparingly in other narration as well.
