I don't want to have to write a regex for all that :)
One of the answers to Sanitize/Rewrite HTML on the Client Side suggests borrowing the whitelist-based HTML sanitizer in JS from Google Caja which, as far as I can tell from a quick scroll-through, implements an HTML SAX parser without relying on the browser's DOM.
Update: Also, keep in mind that the Caja sanitizer has apparently been given a full, professional security review while regexes are known for being very easy to typo in security-compromising ways.
Update 2017-09-24: There is also now DOMPurify. I haven't used it yet, but it looks like it meets or exceeds every point I look for:
Relies on functionality provided by the runtime environment wherever possible. (Important both for performance and to maximize security by relying on well-tested, mature implementations as much as possible.)
toStaticHTMLunder IE8 and IE9.
Highly configurable, making it suitable for enforcing limitations on an input which can contain arbitrary HTML, such as a WYSIWYG or Markdown comment field. (In fact, it's the top of the pile here)
They're serious about compatibility and reliability