With Solaris 10 it should be possible using pfexec and appropriate privileges, but it's more usual to start it as root and use the "User" and "Group" in the config file for normal runtime use as Neo suggested.

Any user can run Apache ( provided the pid file and logs can be written by the user ), but you need extra privileges to run it on the standard ports. If you set the port number > 1024 any normal user could start it. I have in the past allowed certain users to control the Apache server on certain servers without giving them root access by creating an IPFilter to forward from port 80 to an unprivileged port that apache was listening on. To an external user there is no difference but there is no need to grant any extra permissions to the user running the server.