Is there currently some kind of application which can time to time check against a website on whether it has been updated?
HTTP headers include an "If-Modified-Since" request, which causes the server to return only a "304 Not Modified" rather than a whole page. This can be sent by any app capable of HTTP comms.
(my Python senses are tingling)
You could do this pretty easily with a cron job, curl/wget, and a revision control system (such as git or SVN). You would need a *nix system to take advantage of it.
I don't know that anyone has packaged together a simple application to manage this for you though.
I did a quick Google search and found at least one program but I've never used it so I can't vouch for it personally: http://www.google.com/search?q=check+updates+web+site. WebSite-Watcher is the first result at the moment for that query (http://www.aignes.com/).
You can get the Last-Modified HTTP Header, for example (C#):
HttpWebRequest request =(HttpWebRequest)WebRequest.Create("http://www.yoursite.com");
HttpWebResponse response =(HttpWebResponse)request.GetResponse();
Console.WriteLine("Last Modified: {0}", response.LastModified);