Just how worried do you get? And what do you do to try to alleviate your worries? Does it work?
Obviously extensive testing, static typing, code review, and revision control help, but that doesn't mean that your worries are sufficiently low in practice.
I wonder if there's a mental health issue to be studied here with potential solutions specific to software developers.
http://paulgraham.com/start.html
What it means specifically depends on the job: a salesperson who just won't take no for an answer; a hacker who will stay up till 4:00 AM rather than go to bed leaving code with a bug in it; a PR person who will cold-call New York Times reporters on their cell phones; a graphic designer who feels physical pain when something is two millimeters out of place.