I am trying to find out whether conducting military operations without the approval and knowledge of US Congress is a new trend that started with the use of drones or have there been examples of it before?
It seems to me that already the first US military intervention against the Barbary pirates lacked Congressional approval but only had Jefferson's declaration of war. The latest military intervention in Libya seemed to lack full Congress support as described in below article.
The Barbary intervention only followed the Pasha Yusuf Karamanli of Tripoli declaring war on the United States in May of 1801, after Pres. Jefferson refused to make a tribute payment. Jefferson also stated that the Constitution did not authorize any action beyond that of the defensive. Congress would authorize action in 1802, but I cannot recall the name of the act that was passed. However the Quasi-War with France in 1798-1800 was an undeclared war, by both nations.
For further reading:
Lambert, Frank. The Barbary Wars: American Independence in the Atlantic World. New York: Hill and Wang, 2005. (Barbary Wars)
De Kay, James T. Rage for Glory: The Life of Commodore Stephen Decatur, Usn. S.l.: Free Pr, 2007. (Quasi-War and Barbary Wars, through Stephen Decatur)
The operation in Granada comes to my mind as well as the overthrown of Manuel Noriega in Panama. The bombing of Mohamar Ghaddafi's house in Liyba by Reagan also comes to mind. These are some.