This is kind of a holy war-ish question, FWIW. People have strong opinions, and the Qwerty vs. Dvorak thing has been tangled up in some academics' arguments about whether the Free Market is always right.
I've used Dvorak for over two years now, and in my experience:
1. If you spend a lot of time typing on computers you have control over, particularly if your career involves typing, it will probably pay off within a few months. (It works very well with Emacs, IMHO.) If you spend much of your time fixing other peoples' computers or something, it probably won't help you much.
2. If you're genuinely curious about whether it would be worthwhile, it probably will be, even if only for the experience of shaking up really deeply wired habits.
3. Don't do it if you have deadlines coming up! Seriously, don't. Plan on a week or so of typing 5-15 wpm, and any "cheating" during the first week or two will really confuse you. (You'll probably also feel really stupid at first, like you've forgotten how to talk. It will pass.)
4. You will be able to type on a Qwerty keyboard, but switching back and forth within the first month or two will really confuse you. It's not a big deal once you're used to it, though. Having contextual associations ("my keyboard is Dvorak, the one in the school lab (or whatever) isn't") also helps.
What do people here think? Is it worth the time investment to switch?