Let's just end the never-ending debate: It is "Web site" for Government of Canada Web sites, according to recommendations from the Translation Bureau, and "website" just about everywhere else!
You can go online and vote for your preference on many websites. Apparently, 65% of people prefer "website", even though it is not technically correct. (Notice, when I'm not at work I use website. I'd rather be popular than technically correct!)
The Web likes to break rules and create its own way of doing things. It favours content being published quickly and easily rather than content that should be published, yet you'll find lots of useful even incredible content on some sites.
The Internet is a lawless international society. Will they ever tame it?