Hands in the air if you think smartwatches are a product whose time has come. Hands in your pockets, or your purses, if you think most consumers would rather keep using their smartphones for their mobile computing, communication and Web-surfing needs.

Smartwatches have already been on the market for several years, but sales haven’t exactly taken off. That could be about to change, now that Apple has started shipping its Apple Watch, a product some market observers think will be the next big thing, much the same as the iPad...