How to get the number of DOM elements used in a web page

It's quite simple really:

document.getElementsByTagName('*').length

---

If you can ignore older browsers, you could also preserve some of the jQuery-like syntax with:

var $;
$ = document.querySelectorAll.bind(document);
$('*').length;

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.