For as long as I can recall URL’s to websites have always ended in some extension. From the .htm, .html, .php, .aspx, .cgi, and even the strange ?category=2614&sessionid=1jermsmit2you34873691
If you have noticed today, many websites are changing this practice to have URL’s that are friendlier. In fact they have been doing it for many years now. Possibly to optimized search results or just make them look more appealing. Some of the things I have read have even stated it could be useful as a security method so that a ‘hacker’ would not easily guess the backend code of the web application. I wouldn’t advise this as a reason to switch.
Good reasons to switch could be that:
File extensions are ugly, File extensions are irrelevant today, File extensions give away implementation details (back to security), File extensions make life difficult if you ever decide to switch technologies
Regardless of why someone may switch, I personally find it to be pleasant and all the more powerful. This is also why I recently changed jermsmit.com to use extensionless urls also. If your building web applications or simply supporting a website this may be worth looking into. Perhaps you can make a significant contribution to your project by simply making a slight change.