Doing Without the WWW
Most websites, I would wager, are accessible without the "www" prefix to the domain. That's handy. For one, it's a pain to have to say "w-w-w" every time you tell someone the URL of your website. And my habit, when typing in the address of a new website, is to leave it off. It's annoying when I get a "page not found" error. I have to go back and add the prefix, and generally find that the website is there, after all; it just hasn't been configured properly.
I'm not sure everybody would know to do that, and therein lies the bigger problem. If you want folks to find your website, you should make finding it as foolproof as possible. If your website requires you to enter the "www," do yourself a favor and set up your DNS record to point the @ record—the root—at your web server.