I bring my phone with me nearly 100% of the time for the following reasons (in no particular order):
In case of emergency: Unlike 20+ years ago it is difficult to locate a pay phone. In case something happens, I want to be able to contact someone
To track my walking and cycling: Runkeeper is a great app. Instead of counting steps, I get to count miles. And track my progress.
To pay for things: ApplePay is a convenient tool.
To stay in touch with people: Yeah, yeah they can leave a message. And they often do when I don't pick up.
To listen music: I ditched physical media years ago. It is all on my phone
To remain informed: I read the New York Times, Washington Post, The Week, The Wall Street Journal, The Economist, ad other periodicals on my phone
To remain occupied: I get fidgety while waiting in line. See "To remain informed"
This is not to say that I will exhibit sigs of anxiety if I don't have my phone, but it is to say it is a useful tool that I like to have with me.