Enough savings that you don't worry about little things. I just had to fix a wheel bearing on my car $700 later (my mechanic replaced the brakes and a few other small things while in the area) - not a large thing, but for many people that is more than they have saved up.

There are safety nets for big things - not always good ones, but they exist everywhere and so when something major goes wrong you can count on some help. However there are a lot of little things that are both far more likely to go wrong, and also things that it is harder to get help with from any sort of safety net.