Using jQuery I can get easily the number of DOM elemetns used by a web page:
$(\'*\').length;
But not all web sites are using jQuery.
Assuming you mean "HTMLElementNodes" as opposed to "All nodes" (which would include such things as text nodes and also be skipped by your jQuery example) then:
document.getElementsByTagName('*').length
This still requires the use of DOM though. Pure JavaScript can't interact with an HTML document other than as a string of text.