Apache is the leading internet web server, with over 60% market share, according to the Netcraft survey. Several key factors have contributed to Apache's success:
The following websites use Apache or derivatives. Chances are that if Apache is good enough for them, it is also good enough for you :)
>From the Apache website:
The Apache Project is a collaborative software development effort aimed at creating a robust, commercial-grade, featureful, and freely-available source code implementation of an HTTP (Web) server.
The Apache project has grown beyond building just a web server into other critical server side technologies like Java or XML. The Apache Software Foundation, described in the next section serves as an umbrella for these projects.