Most answers bring up the legality of the thing or lack thereof.
Actually, I am not so sure making a local copy of a website strictly for personal use constitutes copyright infringement.
First of all, there is no mention of where the person is located, so we don't even know what copyright laws apply. For instance, Canada and Australia have some explicit positions regarding personal use of lawfully acquired properties, and I believe there are a few rulings in the US along the same line.
Second, by visiting a website, you are automatically making a personal copy using a software called a browser. This is not, I believe, a copyright violation.
Should the user use an offline browser of some kind (like wget) to visit the website and store it on his hard drive, I do not see why this would be prohibited in anyway.
Antecedents and context are also important. If you consider that most websites are archived and made publicly available by the wayback machine (see http://web.archive.org/web/*/http://www.acm.uiuc.edu/webmonkeys/book/c_guide), an usage which is not challenged (archive.org is based in the US), it is pretty difficult to make a valid argument against a private copy intented as a personal reference.
In short, I don't think making a personal copy of a website for strictly private use is a violation of current copyright laws in most countries.
On the other end, distributing the said copy would be a different matter entirely.