Modern warfare, although present in every historical period of military history, is generally used to refer to the concepts, methods, and technologies that have come into use during and after the Second World War and the Korean War. Modern war films, however, are typically considered anything that is post-Vietnam. You'll find lots of modern-day action in these war films.
 

Black Hawk Down (2001)
Black Hawk Down is the story of 123 elite U.S. soldiers who drop into Somalia to capture two top lieutenants of a renegade warlord and find themselves in a desperate battle with a large force of heavily-armed Somalis.
Related Site: Black Hawk Down
Jarhead (2005)
Based on former Marine Anthony Swofford's 2003 book about his pre-Desert Storm experiences in Saudi Arabia and about his experiences fighting in Kuwait. Directed by Sam Mendes, and starring Jake Gyllenhaal and Jamie Foxx.
Related Site: Jarhead Official Site
Home of the Brave (2006)
The day after they get the word they'll go home in two weeks, a group of soldiers from Spokane are ambushed in an Iraqi city. Back stateside, we follow four of them as they struggle to readjust to life at home after a lengthy tour in Iraq.
Related Site: History Channel - Iraq War
Stop-Loss (2009)
A veteran soldier returns from his completed tour of duty in Iraq, only to find his life turned upside down when he is arbitrarily ordered to return to field duty by the Army. Starring Ryan Phillippe, Joseph Gordon-Levitt, and Rob Brown.
Related Site: Six Years in Iraq
Heartbreak Ridge (1986)
Culminating in the 1983 invasion of Grenada, Heartbreak Ridge tells the story of Gunnery Sergeant Thomas Highway, a veteran Marine who's charged with whipping a platoon of misfit Marines into shape.
Related Site: Battle of Heartbreak Ridge

Restrepo
A year with one platoon in the deadliest valley in Afghanistan.

Combat Diary
Provides an unprecedented firsthand account of life and death on the front lines of battle.
Gunner Palace
A group of American soldiers in Baghdad who have taken over a bombed-out palace offer the camera a view on their world. 

Generation Kill (2008)
A Rolling Stone reporter, embedded with The 1st Recon Marines chronicles his experiences during the first wave of the American-led assault on Baghdad in 2003. Starring Alexander Skarsgard, James Ransone, and Lee Tergesen.
Related Site: 1st Reconnaissance Battalion

Over There (2005)
The series follows a unit of the United States Army's Third Infantry Division on its first tour of duty in Iraq, and chronicles the War's effects on the soldiers' families in the United States.
Related Site: Third Infantry Division

Occupation (2009)
The series follows the fortunes of three British Army soldiers from the 2003 invasion of Basra to 2007. Each is inspired to return to Basra for different reasons: one returns for love, one for monetary gain, and one for his belief in the mission to rebuild the country.
Related Site: Invasion of Iraq