I started carrying cash in college, because I knew some women who were fun and spontaneous - but really bad at planning ahead. I finally realized that the best thing to do was 1) fill my gas tank 2) have $40 in my wallet and 3) just block out 6 hours. If someone said, "Let's go to Denny's in Palm Springs in the middle of the night!" I could accommodate. (And yes, that was one of the trips.)
Truthfully, I haven't run into a place that didn't take credit cards since...well, this afternoon. We found a quaint little coffee shop and decided to try it out instead of Starbucks. And they don't take credit cards. Cost about half as much as Starbucks though.
From a security standpoint, I know people who have traveled the world and gotten robbed. The best practice is to have some money so you can give it to them and show them that you don't have any more. They will not believe that you have "NONE." All Westerners are wealthy, somehow. But if you can give them enough to make their day worthwhile, you have a much better chance of being able to go on your way unhurt. You may want to keep a larger amount in a different location.