For me, the primary reason I switched to dvorak was to force myself to touch-type. It worked, but I generally agree that there it doesn't make a substantive difference for most day-to-day tasks.
That said, I really do prefer typing in dvorak. You can feel the difference in number of off-home key presses -- it shows up in your wrists. The difference isn't subtle. "This is a test sentence" has 1 off-home keypress in dvorak and 13 in qwerty. This effect is pronounced enough that passwords, names with foreign spellings, and other types of entropic text are noticeably more awkward to type in dvorak (versus in qwerty, where all text "feels" roughly the same to type). Again, dvorak may not make much of an objective difference as far as health or WPM are concerned, but the feel is enough to make the inconvenience worth it to me.
EDIT: I see the post below me mentions keyboard shortcuts. They were the biggest sticking point for me and they remain the largest compatibility hassle when I have to use a qwerty computer. I would rate the frustration of having to think about shortcuts just slightly below the frustration of having to work with UIs that don't support emacs editing shortcuts, FWIW.