I understand that people who work in emergency services of all kinds and people who are self-employed need to be on their smartphones frequently. But, in general, it drives me crazy when people are more interested in their phones than the live human beings right in front of them. As others have said, it's rude.
I love the convenience of a mobile phone. Mine is a cheap smartphone, just because it was the best buy when I needed a new phone, but I don't use it as a smartphone. Why pay for a data plan that I don't need? Same reason I gave up my landline. Sometimes, if I'm probably going to have time to kill alone, like waiting for a doctor's appointment, I take my iPad instead of a book.
EDIT: This is my 8000th post! You're all invited to celebrate my promotion to Vice Admiral.