I am surprised to find that the NYTimes.com does not provide a canonical domain for its homepage or for its articles (at least, for the small sampling I checked). That is, I get the “exact” same behavior in my browser irrespective of entering http://nytimes.com or http://www.nytimes.com.
There is no shortage of opinion about whether to use a www or no www on your domain. Nearly all agree that your site should respond to both versions.
Before Google announced its support for a canonical URL link tag, it was generally suggested that you should choose one version as the canonical one. This would avoid any possibility of duplicate-content penalties, though an option in Google Webmaster Tools that requests your preferred version suggests that they were never going to penalize for such a thing. Since Google now supports such a canonical URL link tag by which webmasters can specify the canonical url for their page, it might appear that there is no reason at all to choose a canonical domain.
But I can think of at least two reasons.
First, mere branding and consistency suggests that you should have a canonical domain. Your website has a definite address. Use it. Consistently.
Secondly, a cookie set for the www version will not be accessible to the non-www version. As a result, a sequence of visits begun under the www version that included a visit to the non-www version (perhaps by a redirect or a link that hard coded the non-www version) might appear under different sessions, causing all sorts of mischief. Trust me on this one.
The upshot: Sure seems to me like a good idea to canonicalize your domain. Even if the NY Times doesn’t.