Without a domain name (URL or web address), you'd still be able to access and view websites, but only by typing a series of numbers into your browser's address bar (e.g. http://93.174.140.78/ - go on, try it!). Domain names provide a neat, human-friendly and much more memorable alternative, which is why you'll find it almost impossible to find a website without a domain name 'pointing' to it.

You can of course use a domain name for e-mail addresses. There are many free e-mail providers out there (such as Hotmail, Yahoo, Gmail etc) but it's incredibly difficult to find a good address that hasn't already been taken by somebody else.