...and then the web page can pop up another alert before you have time to do anything else.

    for (;;) alert("spam!");

Chrome will, at least, give you an option to disable the alerts if it thinks you're getting them too often, but by that point you're well into scary territory.

Footnote: just tried it in Chrome, and after disabling popups I got a tab which was spinning using 100% CPU and which was completely uninteractive. I couldn't even close it using the x on the tab and I had to kill it via the Chrome task manager. Hmmm...