That's a great question. I've had lots of failures, but most of them turned out to be opportunities so I rarely think of anything I've done as a "failure" per se. But here's a series of failures: I dropped out of college after losing support because of poor performance. Failure. So I spent a few years performing: juggling shows and classes and later clowning. Barely scraped by. Not a success. I went back to school and finished up, got a degree in mathematics. Win! Couldn't find a job. Failure. Got accepted to Ringling Brothers and Barnum and Bailey Clown College. Win! Did not get a contract with the "Big Show" afterwards. Failure. Worked construction and part-time circus jobs for a year...
That's when the fear started setting in. Friends of mine from high school whom I was no less talented than had jobs starting a $50k/year, which in 1992 was a lot of money. I was living in my car sometimes. Fear pushed my to go back to school to get a teaching degree. I took the GRE and did well enough that FSU offered my free tuition and a teaching position to get my masters degree there. Masters degree turned into PhD and suddenly I was a professor in mathematics and mathematics education.
Since then, I've continued to take big chances and push myself. I got tenure and gave it up to move to Norway. I got tenure again at the Norwegian Center for Math Education and gave it to start my own business. I'm struggling with that now and once again on the edge of failure. We'll see what that brings!
About 15 years ago I "decided" I was an artist. (I guess I got tired of waiting around for someone to tell me I was an artist, so I just decided that what I was and would start telling people that.) I wrote children's books and an art book that mostly bomber. But later I made some artwork that won an international prize. I'm still making all kinds of art, and some of it fails badly, but some is ok.
In the classroom I tell students that I fail all the time. You start working a problem and you just try something. Don't care if you fail or not, just try! Then think about what happened, what went wrong? What worked? What new ideas did you get? Then try again. And again. It's basic math problem solving. It's basic for making art. And I think it's basic for being successful in life.