All the running measuring gadgets we use these days--the GPS Garmin Forerunner, Timex's GPS Global Trainer and Bodylink, Nike +, Suunto T4 GPS--can be valuable tools in our training. I love my Garmin Forerunner--no matter where I am I can go out for a run and know how far I went and at what pace. It also stores all my runs and then spits all its information about each run into my computer, so I can analyze my training to my heart's content! Before the days of Garmin, I knew generally what the distances of the routes I ran were and how fast I usually ran them. When I traveled and went out on a run somewhere I had never been before, I would just run a certain amount of time, not knowing the distance, and write in my log that I ran "about six miles" or whatever.
Nowadays we all have our favorite device and I think it's easy to get into the habit of "over-relying" on them. Most elite runners do not use them; they run by "feel," not needing that constant external feedback. Your body doesn't know what a mile is--don't let a device on your wrist define your time spent running. Use it to let you know that you are progressing in the direction you want to go--and leave it at that. You'll enjoy your training and racing much more if you learn to run by feel.