NOW WITH UPDATED INSTRUCTIONS
Facebook Tabs allows you to easily add any website to your Facebook page, just as you can see in the live preview.
The live preview shows a real-life example that is being used by us at UK Film Festivals. It is a WordPress site, but you are not restricted to using a WordPress site, with this, you can show anything.
Are there any restrictions? You should not have a site wider than 800px, as this will not show correctly due to the restrictions set by Facebook, but a responsive site (as seen in the preview) works without a problem. You also need to be able show the website in a frame, which covers almost every website. Some websites, such as Paypal, do not allow this for security reasons though.