I presume you more interested in making the default file executable, rather than index.html specifically.

When no file is specified (as in http://www.example.com/ and http://www.example.com/dir/), the web server looks for a list of files. Usually that list starts with index.html. If you use the following command (Apache's syntax), the web server will use index.cgi as the default if index.cgi is not found.

# Globally, in <VirtualHost>, in <Directory> or in .htaccess
DirectoryIndex index.html index.cgi
[download]

For example, if you have that line in your <VirtualHost>, requesting http://www.example.com/ would be the same as http://www.example.com/index.cgi.