It's kind of shocking when you realize how many conflicts we are currently engaged in. Although US service men are not always in harm's way, people are dying in these conflicts - mainly enemies of our nation but also some innocents.
Here's the list.
Iraq - President Obama inherited this one from Bush. It was covered by the War Powers Act although the various Democratic candidates who voted for it have spent the last seven years trying to backtrack from it. As conflicts go, this one is fairly good at the moment. The country is stable and US soldiers are more likely to die from a traffic accident than from enemy actions.
Afghanistan - "The good war". This is another one that Obama inherited but it is not going so well. After a surge of troops, Obama wants to draw down the troops. The Pentagon wants to keep them for another couple of years. Relations with the Afghanistan government have deteriorated. They don't trust Obama.
Pakistan - This is a continuation of the war in Afghanistan. Again, things are not going as well as they might. Relations with the Pakistani government have cooled quite a bit since we discovered bin Laden in a suburb. At the same time, the Pakistani government is growing tired of being treated as a client state.
Libya - Exactly what is our role in Libya and is it covered by the War Powers Act? That is being hotly debated between the White House and Congress. The Obama administration argues that, as long as Americans are not coming under fire, we are not engaged in hostilities. Congress counters by pointing out that the effort is commanded by an American officer (on loan to NATO) and we seem to be engaged in regime change. Some reports say that we have a more direct role than in being reported and our allies are asking for us to expand our role.
Yemen - We are engaged in a covert war in support of the government against Islamic extremists. We are mainly using unmanned drones so, again, no Americans are in harm's way.
Somalia - We have covert troops training and assisting a new government. We are also hunting down al Qeda operatives. This is mainly a "boots on the ground" action and I bet yuo didn't know about it.
That's the complete list that I know of but I only learned about Somalia from an article in Wired. This is considered to be the model for the future - an outsourced war that gets little press coverage, costs little, and does not require Congressional approval under the Obama definition of the War Powers Act. Expect this list to grow in the near future.