How do you define "succeed"? Does something only succeed if it has the largest market share?

Anyway, Linux has certainly succeeded. In the server and embedded realm it is used a lot.

If you can't find more exceptions you're simply not looking well enough. There are many other exceptions: Wikipedia is open source. And don't forget OSX is based on an open source kernel.

In databases many open source products are used. BerkelyDB is used a lot in applications, so is MySQL in web applications.

Many tools used regularly by developers are open source.