Actually there is one thing (that I know of) that relies on the built in Apache server. That would be the built-in web interface to CUPS, the Common Unix Printing System, that lies at the heart of the Mac printing subsystem.
Honestly most people don't know it's there and even fewer have ever done anything with it. Go to locahhost:631 in Safari and you will either get this error "The web interface is currently disabled. Run "cupsctl WebInterface=yes" to enable it." or you'll get the CUPS web interface.
But Alistair is correct, don't remove it, there may be other dependencies. But you can install other versions of Apache or Nginx or whatever you like side by side with the shipping Apache version with no problems.
In Yosemite and I think Mavericks too Apache is turned off by default and you have to start it from shell commands, if you need a general purpose web server, as the GUI switches have been removed from the Sharing preferences panel.