I rarely run without my running watch or Garmin strapped to my wrist. But yesterday was really hot and humid so I decided it wasn't a good day to worry about how long or fast I was running. So I headed out sans timing device. I have to admit that it felt very strange at first. I kept glancing down at my left arm and was surprised to see a naked wrist. But it was somewhat of a relief and a little bit more relaxing to not be thinking about how fast or far I was going. I didn't get upset that the heat was slowing me down because I really didn't know my pace. I started to pay attention to other things like how much water I was drinking, my breathing, and my form on the hills.
If you're a slave to your running watch, I'd definitely suggest occasionally running without it so you're running based on how you're feeling, not the numbers on your watch.