Yes, manually accept and deny cookies using your browser.
For IE -> Tools -> Internet Options -> Privacy -> Advanced ->
Tag "Automatic cookie processing disabled"
Direct cookies -> Ask
Indirect Cookies -> Deny
Or if you use Firefox:
Tools -> Options -> Privacy - Cookies:
Tag "allow sites to set cookies"
Tag "For the originating site only"
Select "Ask me everytime"
Now you're going to have to learn which websites will work without cookies and which don't. You will also have to learn what cookies you can safely accept and which you can't. Experience 'll tell. Or buy software that automatically removes cookies, but this the safest bet because they will never have penetrated your defenses...