var html = "<p>Hello, <b>World</b>";
var div = document.createElement("div");
div.innerHTML = html;
alert(div.innerText); // Hello, World
That pretty much the best way of doing it, you're letting the browser do what it does best -- parse HTML.
Edit: As noted in the comments below, this is not the most cross-browser solution. The most cross-browser solution would be to recursively go through all the children of the element and concatenate all text nodes that you find. However, if you're using jQuery, it already does it for you:
alert($("<p>Hello, <b>World</b></p>").text());
Check out the text method.