One would think google would have the brains to figure out that example.com = www.example.com. But even in webmaster tools, you have to register both forms of your name in order to tell them you only want to use one. (Yes, technically www. is just another subdomain. But honestly now, is there any attested case of the two being genuinely different sites?)

Be that as it may, the redirect is so simple, it would be foolish not to institute it. Besides, a domain-name-canonicalization redirect will also eliminate rare but unwelcome events, like other people pointing their DNS at your server.

But honestly now, is there any attested case of the two being genuinely different sites?)

I have seen that, although it was a few years ago. The situation is rare but not imaginary.

the redirect is so simple

Yes. Might help, won't hurt. Just do it.

not penalize, filter - and you don't want to take chances the wrong version is filtered.
so what they said - redirect the noncanonical requests to the canonical url.

I thought this whole thing was a joke because it seemed hard to believe that Google can find "complicated" or "confusing" the simultaneous use of www.mydomain.com and mydomain.com for a website.

Lucy24, Buckworks and Phranque... thank you very much for taking the time to enlighten me on this issue! :)

While you're at it, try to make sure that URLs such as

Example.com/index.html
Example.com/somedirectory/index.html

Resolve to

Example.com/
Example.com/somedirectory/

I prefer my URLs without www., and I prefer to always use the trailing slash. It's okay if your preferences aren't the same, but the key here is to be consistent.

The fewer URL variations that are in circulation for the same content, the better.

Ok I'll check that. I have the same preferences as you. ;)

Thank you Buckworks! :)

I also prefer my URLs without www., and I prefer to always use the trailing slash; but is this the preferred preference among the core of developers?

From a marketability standpoint, saying 'www' is an outdated mouthful in my opinion, although I am seeing an emergence in 'www' use in promotions of websites with new domain extensions that are confusing.

is this the preferred preference

No, in fact it's the kind of thing people get into fistfights about ;) There are actually three options, not two:
-- filename with extension (whether truthful or otherwise): example.com/directory/page.html
-- filename without extension: example.com/directory/page
-- filename with trailing slash (whether or not it represents a physical directory): example.com/directory/page/

Which form you use is probably less important than making sure only one version resolves to a page, while others are redirected as appropriate. Anything in the form "page/" will lead to search-engine requests for "page" (without slash) and for "page/index.html", because they don't know whether it's a real, physical directory. I don't know what other requests there will be if you're extensionless, but I wouldn't be surprised to hear they try it with a slash, at least. Someone will know.

I like a balanced-looking name, so it might be either with or without www depending on what else is in the domain name, like "www.twowords.com" vs. "completemultiwordphrase.com".

Also note that the trailing slash only applies to deeper URLs. There's no difference between "example.com" and "example.com/"; that particular slash is supplied-- or not-- by the user's browser. It has no effect on the request that reaches the server, and you can't change it from your end.