Short of any other telling signs (e.g. a "powered by [insert system name here]" comment in the footer) one option is to examine the source code or HTTP headers. For example, the MODx content management system inserts a "MODX_MEDIA_PATH" variable into the Javascript output. The BBC website uses an in-house created system which inserts a version number into a comment somewhere in the source code.
You can also look at the page URLs providing the site is not using any rewriting technologies. ASP.NET-based systems prior to version 3.5 end their URLs with ".aspx." shoutlife.com uses ".cfm" which is Cold Fusion.
If the website is powered by PHP, and the option has not been disabled by the site administrator, PHP inserts a PHP version number into the HTTP headers. ASP.NET inserts a "X-Powered-By: ASP.NET" header into the response headers.
You can use something like the Firebug add-on for Firefox to view the request and response headers. As for shoutlife.com, there are no telling signs in the source code or HTTP headers so it is likely a home-brew solution.