Well, the full Anaconda Plan (the one envisioned by General Winfield Scott) was never really implemented. His plan had much more emphasis on gradual political and economic pressure and less on wholesale conquest. His idea was that this gradual pressure would bring the rebel states back into the Union with a minimum of death and destruction. The problem is that at the time he originally proposed the plan, Union temperament (for lack of a better word) was strongly against such a plan. They believed that the rebellion could be put down quickly - the slogan "On To Richmond" was prevalent. In addition, the army and navy weren't in good enough shape in the early war to be able to implement the strong blockade (on land and sea) that would be necessary for the plan.

General Scott was replaced by George McClellan in July 1861, and the plan was essentially shelved. While the navy blockade was established fairly early in the war, the various Union armies in the field didn't have the coordination necessary for a simultaneous advance until Ulysses S. Grant was appointed General-in-Chief in 1864. By that time, the North had committed to a total war, far beyond the scope of what Scott had intended in his original plan.

TL;DR: The Anaconda Plan was never really happened.