One of biggest wins of hyphenation from my (purely subjective) point of view is that it enables the copy to be fully justified (left and right).
I have never liked having ragged right margins. I find it visually jarring and, to my eyes, it makes the copy look somewhat unfinished.
I know that H&J has traditionally been frowned upon on the web, not least because of the unsightly rivers of white-space that can end up appearing in the text, but with hyphenation and a good rendering engine there’s no reason why it should not be used.
I’ve found today’s WebKit-based browsers handle hyphenated and justified text very well, with no obviously over-large blobs of white-space in the content.