I have used the add-on "Self-Destructing Cookies"* to handle normal cookies, with only a few non-tracker web sites on my whitelist. It has been surprisingly non-intrusive. It works by removing all cookies from domains that have not been visited for (by default) ten seconds, resulting in very few cookies lying around. I am not aware of an equivalent add-on for non-Firefox browsers.

* https://addons.mozilla.org/en-US/firefox/addon/self-destruct...