No, you can access your website's index page through both http://www.yoursite.com or http://yoursite.com. An exception to this rule is with subdomains, which require you to NOT have the WWW prefix (i.e. http://subdomain.yoursite.com is ok).
For detailed information on how URIs (Uniform Resource Identifiers) work, check out this excellent article: http://en.wikipedia.org/wiki/URL
