It is mostly used to separate cookies from the other subdomains.
You can always use an 301 redirect to redirect the short domain to the one with
www., that way your users don't have to type it.
This will allow you to create sub-domains that are cookie-less for static data serving. Without a
www., cookies are served on all sub-domains. Therefore, if you are not using the
www., you need a completely separate domain name to have a cookie-less domain versus just using a sub-domain.
Other than that, choosing between keeping the
www. or not is just a question on which one you prefer. Just make sure to redirect the one not chosen to the other one using a 301 redirect.
To explain, setting a cookie uses a hierarchy for how the cookie is propagated to domain.
For example, setting a cookie to
example.com effectively allows the transfer of cookies to:
Versus setting a cookie to
www.example.com only allows the cookie in those situations:
By using a
www. you are allowing yourself to use sub-domains to have different cookies from the main site (and none at all if so desired).
www. (or another sub-domain), all cookies set on the domain will propagate to the sub-domains.