Do digital watches work in space?

not sure about standard, but digital watches can, yes.

http://www.star2star.com/company/space-museum/time-in-space

Of course they can. Why wouldn't they? There would be a small relativistic effect that would result in them being behind when they returned to Earth.

Do you mean in the actual vacuum of space, or in a contained environment like a functioning space station?

If digital timers didn't work I imagine there would be a lot of trouble out there instrument-wise.

Not to mention if there's some reason (other than a dead battery) for digital watches not to work, more than likely all the other equipment that relies on the same technology would also not work -- which is probably a large proportion of what's in a modern space station.

Digital watches work fine. So do analog ones. One or the other, or both, have been on every space mission. Curious question though, what prompts it?

Jeff