The first thing to acknowledge is that there is nothing special about attacks from an organization such as anonymous.
Please note that I'm not saying that you should not try to protect yourself from those hacking groups. What i am saying is that, unless you are specifically targeted or are part of a target scheme by a group, those organizations' attacks will be the same as the many attack attempts that security professionals see every day.
The only time that a group such as anonymous will actually change security initiatives is when you start looking into APTs (advanced persistent threat). If you are not familiar with the term, or even if you are, i suggest that you take some time researching what an APT is (there is no clear definition).
The best defense against that kind of threat is the bolstering of current industry security practices. This means a combination of tools; use security information/event management (SIM/SEM) technologies, intrusion detection/protection system (IDS/IPS) technologies, network behavioral analysis (NBA) technologies, proxys, anti-virus, firewalls, etc. Making a more comprehensive solution and paying more attention to changes in your environment is what needs to be done.
The idea that some organization is deliberately using a multitude of different technologies/techniques together to attack your system requires the use of a multitude of defense technologies/techniques that are correlated to defend against it.
So, the simple answer is this... There is no different way to defend against organizations such as anonymous, use the tools and techniques that already exist and keep a watchful eye.