My understanding of EBO is that it tries to move away from the "typical" military approach of simply aiming to inflict overwhelming damage on the opponent, and specifically, on his fielded military forces. At the operational level, this means considering what the overall campaign objective is and creating a plan that aims to achieve this effect as efficiently as possible.
Perhaps the most famous example is the first Gulf War. John Warden wanted to conduct a purely strategic (this does not mean nuclear) campaign against Saddam's control apparatus to isolate him as a leader. His plan was to completely ignore the deployed troops in southern Iraq and Kuwait and effectively run a decapitation plan. Without effective leadership, Warden proposed that the deployed troops would revolt/retreat/surrender thus achieving the campaign goal: removal of Iraqi presence in Kuwait.
In the event, he was overruled (well, he was only a colonel) and only a small proportion of the Desert Storm sorties were strategic. Nevertheless, we all remember the footage and effectiveness of what was done in Baghdad. Within 24 hrs, the capital's infrastructure had been brought to a halt and Saddam spent most of his time running from one hideout to another. EBO - QED.
At the tactical level, STH's comments are also examples of EBO. To muse for a moment, at the Grand Strategic level, one could argue that Reagan's economic arms race with the soviets was also a good example of EBO - Goal: win cold war; Solution: bankrupt enemy; Avoid: blood and destruction on the North German plain.
Possibly all b**ll*cks, just my 2d worth.