Do you ever find yourself frantically trying to fish your phone out of a pocket or purse to find out whether that beep or buzz from the device is an important call, text or email—or just something you can ignore? What if you could simply glance at your watch to find out?

Well, now you can, thanks to a new $150 digital wristwatch called Pebble that connects to an iPhone or Android phone wirelessly and displays notifications and previews of calls, texts and emails. Not only that, but the Pebble can control music playback on...