Most current web servers with PHP & MySQL installed will be capable of running WHMCS. However, the specific system requirements are:
N.B. We've been finding that Ioncube does not function properly with PHP 5.3 & WHMCS yet and so you will need to run PHP 5.2.x or lower until an Ioncube update is released for this issue.
If you would like any more information or need help in determining if your server meets these requirements, please contact us.