I have one but the battery died and I'm pretty lazy when it comes to looking up the size and replacing it. One of my roommates has one she uses often, the other wears hers constantly.
I wouldn't say they're outdated at all. They're unisex (yeah, they do make specific for each gender too), and come in a myriad of sizes, shapes, styles, and functionalities. You can even get an analog watch for your kid and make him have to know how to read a real clock instead of just convenient numbers.
Lots of people don't have cell phones. In some classes and places you're not allowed to have them on, so you wouldn't be able to check the time. They also run out of battery significantly more rapidly. I have a personal issue with how bright the back light is at night or when I'm watching a presentation or something, people KNOW you have a phone and it mars your night vision for a time.
Also, if you're working with your hands, it's often more convenient to just look at your wrist instead of breaking the flow of what you're doing to stop, pull out your cell from wherever it's at, and turn on the display, then put it back and resume.