Do copyright dates need to be updated?

There is no reason at all for an individual to update the copyright year, because in the U.S. and Europe the life of copyright is the life of the author plus 70 years (50 years in some other countries like Canada and Australia). Extending the date does not extend the copyright. This also applies when a page has multiple contributors none of which are corporations.

As for corporations, Google doesn't update their copyright dates because they don't care whether some page they started in 1999 and updated this year falls into the public domain in 2094 or 2109. And if they don't, why should you? (As a Googler, now an ex-Googler, I was told this was the policy for internal source code as well.)

Your OCD is to blame :)

You do not have to put anything about copyright on your page - copyright automatically applies until you explicitly license it otherwise. Copyright also applies for a preset number of years as determined by international treaties. I do not know what the exact number of years is, but it is a lot, so there is absolutely no point in updating the year in your copyright notice.

Technically, you should update a copyright year only if you made contributions to the work during that year. So if your website hasn't been updated in a given year, there is no ground to touch the file just to update the year.

The copyright notice on a work establishes a claim to copyright. The date on the notice establishes how far back the claim is made. This means if you update the date, you are no longer claiming the copyright for the original date and that means if somebody has copied the work in the meantime and they claim its theirs on the ground that their publishing the copy was before your claim, then it will be difficult to establish who is the originator of the work.

Therefore, if the claim is based on common law copyright (not formally registered), then the date should be the date of first publication. If the claim is a registered copyright, then the date should be the date claimed in the registration. In cases where the work was substantially revised you may establish a new copyright claim to the revised work by adding another copyright notice with a newer date or by adding an additional date to the existing notice as in "© 2000, 2010". Again, the added date establishes how far back the claim is made on the revision.