Someone recently asked about the usage of hyphens in response to my post about semicolons. First of all, I'd say that technically speaking, I think the question revolves around dashes, not hyphens, although depending on the word processor, dashes are created by using hyphens (two, to be exact). Now the question posed was how they differ from semicolons. Simply put, dashes are used to interject additional information into the text with emphasis. In fact, text set off with dashes doesn't even have to be an independent clause--you can put whatever you want here, almost!
Semicolons, on the other hand, are not necessarily used for emphasis or even the addition of information, and they always, unless used in a list, require a complete, independent clause. The semicolon is used to stress the relation of the current clause with what went before. A dash is used to offer additional information, much like commas or parentheses can be used. But the idea is that a dash means you want to emphasize what you're saying while commas or parentheses are used to offer additional information that can be ignored.
When I use or read a dash, I imagine the person to be speaking that bit emphatically--with emotion. If I read something in parentheses, I imagine the speaker to be sneaking that bit in a hurried and low voice, almost as if the speaker didn't want you to lose sight of what is being said but thought it worth mentioning all the same.
Recently, I've seen the use of the word orthagonal in various technical discussions when I think the meaning desired by the writer is more along the lines of tangential or peripheral. The reason I bring it up is that this is what the parentheses are good for--mentioning information that is tangential. Conversely, if one uses dashes, one wants the reader to pay attention--it is integral that this be read. So I'd say the key associations are:
parentheses - tangential and hurried
dashes - integral and emphasized
(Oh, and by the way, a hyphen is used to connect multi-word terms and, in the past, for line continuation. It's not the same thing as a dash, which introduces a phrase, although, as mentioned, you can use two hyphens to indicate a dash.)