Yes, you should take a cell phone with you on a day hike, and most people will anyway. Here's the right way to do that.
First, put a full charge on the phone battery. Second, even if you're in an area with cell coverage, turn off the phone and stow it in your pack. Don't turn it back on until the hike is over, or until there's an emergency. Use a GPS unit to navigate, use a camera to take pictures, and so on.*
Why? Three reasons.
First: hiking has a psychological benefit, but only if you unplug from modern society. Once you do, your brain shifts its focus to the natural world. As you take in the greens of trees, the songs of birds, and the changing sky and wind, your brain gets a much-needed break from your everyday worries. (Similar moralizing possible about iPods and other entertainment devices.)
Second: even if you don't want to unplug from civilization and immerse yourself in nature, yakking on a cell phone is unfair to hikers who hope to do just that.
Third: in an emergency you'll need to call for help, and then you may need to stay in touch with rescuers for hours, possibly days, until they find you. You can't do that if you drained your battery by keeping your phone on.
As part of your backup gear, a fully charged cell phone makes a lot of sense. As part of your ordinary hiking, making and receiving cell phone calls makes no sense at all.
*If you insist on keeping your phone on to take pictures and such, putting it in airplane mode will reduce battery drain and block phone calls. Also, you can increase your margin of safety by taking along a portable recharging unit.