I would have to say the Executive Branch is the most powerful today, even though the system is designed for the three branches to be roughly equal. The power of the President really expanded during George W. Bush's tenure, and the ways in which both Executive Orders and signing statements have been used recently represents that expansion. So does the Patriot Act and increased power for executive law enforcement agencies.
While they had something like congressional approval, and continued funding, Vietnam, the Persian Gulf War and the current Iraq and Afghan Wars are all undeclared by Congress. The President simply ordered in troops and Congress supported it, and the Supreme Court never ruled the action unconstitutional.
The founding fathers designed the government to have what is known as a "balance" of power between all three branches. So no one branch is supposed to be more powerful than the other. Is this true in reality? You would get a variety of opinions on this one. Some feel that the Judicial Branch is too powerful today because although the courts are supposed to interpret the laws, some accuse them of actually making laws in their decisions, etc. Other people would argue that the Executive Branch is too powerful today. The Congress is supposed to declare war, however, but it is the president's job to protect the people, so if he/she feels that protection entails a "police action" or "conflict", he/she can declare this without an actual declaration of war. The Congress, however, controls the money, so some people think that this branch is the most powerful. No matter what the president winds up doing, he/she must get the money to pay for it from the Congress.
There are some really good references regarding government here on enotes.