Yes, absolutely! You can run PHP, python, ruby, perl, lisp and tcl applications on our system, as well as many others.
We have custom integration for PHP, as well as support for using FastCGI, SCGI, and HTTP to speak to an application server written in the language of your choice, like Django, Ruby on Rails, or Node.JS.
CGI has fallen out of favor due to its drawbacks; all of those alternatives didn't emerge because it was so great. However, it still fills a need and works fine here; you can simply put a CGI script in your web space with a .cgi extension, and mark it executable.
We update our support for programming languages very frequently. Check our home page for links to current example configurations.
SSI (server-side includes) can be used by naming your files with a .shtml extension.