I remember when I started in photography, I was using a point and shoot camera. Like most people, I carried it around, and when I saw something interesting I pulled it out, aimed and snapped the photo.
Then as I got more serious I read in a book that to get really sharp photos you needed to use a tripod. When? Always! Well, as silly as it seemed putting my little camera on a tripod, I forced myself to do it. I discovered that not only were my photos sharper, but my composition improved! The simple act of taking the time to set up the tripod meant I was paying more attention to my subject and watching out for details like what was in the frame, the angle of the shot, and keeping those horizons straight.
When I switched to a dSLR, using a tripod became even more important because I was not used to the heavier camera, and camera shake was even more likely to become a factor.
Now I'm so accustomed to taking my tripod everywhere, I can't imagine leaving home without it.