To begin with, I don't see the term effectiveness used often, other than in management books or consultants. I think the reason being is that while there is an implicit understanding of efficiency, the same is not true of effectiveness.
As per some of the examples given by the others, in a practical sense, efficiency is unbending, while being effective almost always means adjustments in response to the inevitable deviations that happen. Effectiveness is applying the right solutions to the unforeseen events and obtaining the desired end result.
Along the way true efficiency is a rare thing to achieve without adjusting the end goals, so compromises are made, usually impacting both efficiency and the end result.
Ultimately I would say that in most situations, maximizing efficiency while achieving the desired goals is true effectiveness. So in sense, efficiency is almost always an implicit metric as part of the overall solution.
