Well that depends on the superpowers. There are some pretty bad ones out there.
I suppose if I had some of the major ones strength, flight, invulnerability, etc. I would wind up telling some people, just people I could trust. Through if I was the only one in the world with those powers I would go to my death bed with the secret.
Say you had Superman's powers, you could pretty much do whatever you wanted whenever you wanted, having a "secret identity" is the only way to do anything normal after people know what you can do.