Mac OS X comes with Apache, and I installed PHP and MySQL locally so I can work without an Internet connection - most of the website stuff I do uses PHP and so I must use a web server. But even if you don't use PHP, you may as well use Apache since you get it "for free" with OS X.

My text editor of choice is TextMate, whether for PHP/HTML, C++, TeX, or whatever. When I do have an Internet connection, I use Cyberduck (a secure FTP client) in conjunction with TextMate to edit pages as if they existed on my local disk. As for copying an entire website for offline editing, you can certainly use Cyberduck or any other file transfer program (i.e. scp with the -r flag) to copy the files to your local disk and back again when you're done.