Okay, so this is a very interesting question. There are even websites that discuss this: http://no-www.org/ and http://www.yes-www.org/.
http://www.yes-www.org/ has a page 'Why use www?'. From their website:
You should use www because today you have a small web site, and
tomorrow you want a big web site. Really big.
The technical reasons to use www primarily apply to the largest web
sites which receive millions (or more) of page views per day, web
sites with a large number of services across several subdomains, and
virtually any web site hosted in “the cloud” by an application service
provider.
Heroku, for instance, strongly recommends against using naked domains.
When using a provider such as Heroku or Akamai to host your web site,
the provider wants to be able to update DNS records in case it needs
to redirect traffic from a failing server to a healthy server. This is
set up using DNS CNAME records, and the naked domain cannot have a
CNAME record. This is only an issue if your site gets large enough to
require highly redundant hosting with such a service. But who doesn’t
want their site to get that large? In order to not use www, you will
have to run your own server farms and you will be unable to use such
services to their fullest extent. (See also: Why does Heroku warn
against “naked” domain names?)
Another reason has to do with cookies. One common web site
optimization is to serve static content from a subdomain, such as
static.example.com. If you are using www, then this is no problem;
your site’s cookies won’t be sent to the static subdomain (unless you
explicitly set them up to do so). If you use the naked domain, the
cookies get sent to all subdomains (by recent browsers that implement
RFC 6265), slowing down access to static content, and possibly causing
caching to not work properly. The only way to get around this problem
and keep the naked domain is to buy a second domain name just for your
static content. Twitter, for instance, which does not use www, had to
buy new domain names just for static content. Of course, if you
explicitly share your cookies across all your subdomains, for instance
to implement single sign-on across various services on subdomains of
your site (Google does this), then you too would have to buy a new
domain name in this circumstance anyway. (See also: What’s the point
in having “www” in a URL?)
Speaking of cookies, if you decide to use the naked domain, but want
to put services on subdomains and share cookies between them, you’ll
quickly find out that it doesn’t work right in all cases unless you
have a subdomain set the cookie — and then it doesn’t work for the
naked domain. The fix for this is to use RFC 6265 (formerly RFC 2965)
cookies, which can be shared between the naked domain and subdomains,
but some popular web application packages still do not implement RFC
2965 properly or at all, let alone RFC 6265. (See also: Can
subdomain.example.com set a cookie that can be read by example.com?)
You may not run into any of these issues today, but as your web site
grows, you eventually will. Using www today and in the future makes
you more prepared to handle the challenges of growing a web site
beyond a single server. It can be done without using www in many
circumstances, but it’s much easier with.
As for SEO, there are no benefits of choosing www or no www.
