Who has the power to declare war?

Generally speaking, the government of a nation has the power to declare war. Typically, the constitution or other establishing laws of a nation will specify which part of the government can declare war. Thus, in some nations, such as the United States, the act of declaring war may be reserved to a legislative body. In other nations, the power to declare war may rest in an executive or head of state. In nations without a constitution or establishing laws, or where the power to declare war is not specifically reserved, the sovereign (the person or entity with ultimate decision making authority for a nation, such as a monarch) has the power to declare war.  
If the question is asking who specifically in the government of the United States has the power to declare war, then the answer is that the power to declare war is specifically reserved to the Congress under Article I, Section 8 of the United States Constitution. Further, Congress has the power to fund the U.S. military and any continuing action by the U.S. military, giving Congress more oversight regarding the use of force than just the power to declare war. The U.S. President does have the power to use the military for operations of a limited scope without prior approval by Congress, but such use is subject to various time restrictions and reporting requirements.
Finally, continuing military operations by the United States military that are carried out absent a formal declaration of war are not prohibited if Congress authorizes such continuing operations. The authorization in such instances is often granted implicitly through the Congress’s power to fund, or not fund, the U.S. military and its operations rather than through any formal proclamation. And so long as Congress approves ongoing funding for military operations, such can continue indefinitely, even absent a formal declaration of war. So while Congress does have the sole power to declare war under the U.S. Constitution, it does not have to do so in order for the U.S. military to wage a war.