The Conficker Working group has created a web page that uses knowledge about conficker blacklisting to allow you to easily determine if your computer has been infected.
All you need to do is navigate to the website http://www.confickerworkinggroup.org/infection_test/cfeyechart.html. If you can see all six images in the eye chart, the computer that you are browsing from is likely not to be infected (your results may vary if you are using a proxy).
If the page doesn't load at all, the site has too much traffic. If you are infected, you'll just be missing specific images in the "eye chart".