How to get the entire document HTML as a string?

MS added the outerHTML and innerHTML properties some time ago.

According to MDN, outerHTML is supported in Firefox 11, Chrome 0.2, Internet Explorer 4.0, Opera 7, Safari 1.3, Android, Firefox Mobile 11, IE Mobile, Opera Mobile, and Safari Mobile. outerHTML is in the DOM Parsing and Serialization specification.

See quirksmode for browser compatibility for what will work for you. All support innerHTML.

var markup = document.documentElement.innerHTML;
alert(markup);

You can do

new XMLSerializer().serializeToString(document)

in browsers newer than IE 9

See https://caniuse.com/#feat=xml-serializer

I believe document.documentElement.outerHTML should return that for you.

According to MDN, outerHTML is supported in Firefox 11, Chrome 0.2, Internet Explorer 4.0, Opera 7, Safari 1.3, Android, Firefox Mobile 11, IE Mobile, Opera Mobile, and Safari Mobile. outerHTML is in the DOM Parsing and Serialization specification.

The MSDN page on the outerHTML property notes that it is supported in IE 5+. Colin's answer links to the W3C quirksmode page, which offers a good comparison of cross-browser compatibility (for other DOM features too).