I like watches, but it goes further for me. I have meetings where I need to keep track of the time, and I don't want to be rude by taking my phone out of my pocket to check the time.
Yes, I said it, I'm old school enough to admit that I think it's rude for one to take his phone out of his pocket during a one on one meeting. Frankly, any meeting that isn't an informal one between coworkers.
I turn my ringer off, and leave my phone in my pocket when I'm with someone while conducting business.
Looking at a phone (for the time; at an email or a text message; etc.) tells the other person that he's not the most important thing on my mind at that moment; and it rude.