How to comply with the EU web cookies directive?
If your website or business is based in the European Union then yes. The extent of the information depends on the interpretation of the EU law, but in most cases this needs to be a list of cookies your website sets with a brief description of their purpose.
You can start with the cookies report provided by WebCookies.org and then add the informative and legal content specific to your website. British International Chamber of Commerce published a guidance document ICC UK Cookie guide that comes very handy for writing the legal part.
For most websites in most EU countries it should be sufficient to provide a clear, easy to read information on what cookies your site sets and what is their purpose (example on ICO website). To do that, you need to actually know what cookies sets — and this is where WebCookies.org helps a bit. You can scan your website and use the obtained results as a starting point to develop full documentation of cookies used.
Note however, that the road to the directive was long, bumpy (see NoCookieLaw) and full of rather complicated legal discussion (see Opinion 04/2012 on Cookie Consent Exemption) which is not always consistent with technical understanding of how cookies work.
In addition to that, there's one Directive and 27 Member Countries in European Union to implement it, and each country took slightly different approach. As result these local implementations can substantially differ from each other. So if you need to be certain about your compliance against the laws in your jurisdiction, consult a technology lawyer.