Apple’s default alarm behavior on iOS is to have the alarm go off indefinitely, so if one wants to use the iPhone or iPad alarm on Shabbat, one has to use a third-party app like this one that shuts the alarm off by itself. The only other thing I can think of to do with an iOS device on Shabbat is play media (like music) on a playlist, which would of course have to start before Shabbat.
You could theoretically also play media that way from the watch. We don’t know what third-party developers will be able to do yet, but it may be possible to make a Shabbat timer that works the same way. (Update: It looks as though full-fledged apps like the ones you’d need to write to make a Shabbat timer won’t be possible until the second version of WatchKit.)
You wouldn’t be able to wear the watch on Shabbat under normal circumstances because the screen sleeps until you lift the watch to look at it, which causes it to light up. Since the device is unreleased, we don't actually know if it's possible to keep the display from sleeping. Assuming it’s possible, though, the first-generation watch is almost certainly not going to make it through Shabbat with the screen on. Apple has indicated that the battery life will only last through one day of normal use, and that’s with the screen off at all times except when the user is looking at it.