Hopefully everyone out there does this already, but there's some that might not. I recommend always bringing a phone with you when you are out doing your training. Even if you're only going out for a few miles and don't think that you are going to be far from home.
When I'm out on my bike, I always have my phone with me, and I've had to use it a few times. The obvious reason why you might need to call someone is that you got a flat tire. Hopefully you carry a spare tube and some CO2 cartridges so you can change a flat. But I've had the unfortunate luck of getting two flats at the same time! Since I only carry one spare tube with me, I was unable to repair the second tire and therefor needed a ride home. Bummer. Another reason to have your phone on the bike is in the case that you have a little crash. Bike crashes aren't all that uncommon, and you never know if you're going to bend a wheel or break a chain. There's many other reasons to carry a phone on the bike. Don't waste your time thinking about all of them, rather spend your time figuring out how to get your phone on your bike!
When I run, I stash my phone in my water belt. I don't typically venture out too far from home when I'm running, but there's always that chance of twisting an ankle or pulling a muscle. I don't usually have an excess amount of time, so if I had to limp home halfway through a run I'd probably be really late for something.
Lastly, you never know if someone is going to need to get in touch with you. My rule of them is that I typically screen my calls while I'm training. If it's someone who knows I'm out training and they are still calling, I figure it might be important (like when The Wife calls me). If I don't know why they're calling it, it let it go to voicemail and figure that if it's really important, they'll call again.
It's mostly a safety precaution, but carrying your phone is one of those things that might give your or your family some peace of mind while your running or riding around out there with all of those crazy drivers. Do yourself, and your family, a favor and figure out how to start bringing your phone with you when you train.