Perpetual war
On September 16, 2001, in a speech, President Bush referred to the war on terror as a crusade. He said:

 No one could have conceivably imagined suicide bombers burrowing into our society and then emerging all in the same day to fly their aircraft - fly U.S. aircraft into buildings full of innocent people - and show no remorse.  This is a new kind of  -- a new kind of evil.  And we understand.  And the American people are beginning to understand.  This crusade, this war on terrorism is going to take a while.  And the American people must be patient.  I'm going to be patient.
Andrew Bacevich described Bush's naming of the war on terror as a crusade as something which does not make the war separate, rather something that shows that it is part of an "eternal war."

War memorials: With the advent of perpetual war, communities have begun to construct war memorials with names of the dead while the wars are ongoing. The Northwood Gratitude and Honor Memorial in Irvine, California was dedicated in 2010 to American troops who lost their lives in the wars in Iraq and Afghanistan, with space for 8,000 names (approximately 4,500 used at time of construction) and the intention to update it yearly.

Views of influential writers: 

Sun Tzu: Ancient war advisor Sun Tzu expressed views in the 6th century BC about perpetual war.  The following quotation from chapter 2, Waging War, of his book The Art of War suggests the negative impacts of prolonged war:

Sun Tzu said:  ... When you engage in actual fighting, if victory is long in coming, the men's weapons will grow dull and their ardour will be damped.  If you lay siege to a town, you will exhaust your strength ... There is no instance of a country having benefited from prolonged warfare ... In war, then, let your great object be victory, not lengthy campaigns.

Alexis de Tocqueville: Historian Alexis de Tocqueville made predictions in 1840 concerning perpetual war in democratic countries.  The following is from Volume 2, chapter 22, "Why Democratic Nations Naturally Desire Peace and Democratic Armies, War", 18th paragraph, in his book, Democracy in America:

No protracted war can fail to endanger the freedom of a democratic country. Not indeed that after every victory it is to be apprehended that the victorious generals will possess themselves by force of the supreme power, after the manner of Sulla and Caesar; the danger is of another kind. War does not always give over democratic communities to military government, but it must invariably and immeasurably increase the powers of civil government; it must almost compulsorily concentrate the direction of all men and the management of all things in the hands of the administration. If it does not lead to despotism by sudden violence, it prepares men for it more gently by their habits. All those who seek to destroy the liberties of a democratic nation ought to know that war is the surest and the shortest means to accomplish it. This is the first axiom of the science.

Fiction: In George Orwell's novel Nineteen Eighty-Four, the three superstates of the world, Eurasia, Oceania and Eastasia, are said to be in a perpetual state of war with each other. The attacks are in the form of rocket attacks (similar to the V2 Attacks on London in WW2) although it is implied in the book that the attacks could be launched by the home Government against their own people in order to perpetuate fear and hatred of the enemy. Therefore, perpetual war may in fact secretly be a strategy used by the state to continuously promote its own political agenda. However, the military attacks are limited to the non-aligned areas (North and Central Africa, India etc.), an example of this is The Malabar Front (India) where Oceania won a victory against Eurasia.
In the Doctor Who series Genesis of the Daleks, the Kaleds and the Thals are in a perpetual state of war and have been for 1000 years.  This state of war finally results in both sides occupying one city each on either side of mountains, and leads to both sides supplies being so completely ravaged by the war that both sides have a collection of black powder weapons, modern and futuristic weapons and armour.  It is out of this war that the Daleks are created by Davros.
Also in the Doctor Who series, the Sontarans and the Rutans have been in a perpetual state of war for over 50,000 years. There appears to be no end in sight, with each side continually attempting to completely obliterate the other. This has resulted in either side constantly gaining and losing territory (including the Milky Way galaxy, which is known in Doctor Who as the "Mutter's Spiral").
And again in Doctor Who in Destiny of the Daleks, the Daleks and the Movellans have basically been drawn into an Endless War, due to their battle computers both giving a logical set of orders, only to have one set countered by the other battle computer with an equally logical set of orders.  As both sides are using logical instructions, neither side could win as both sides would be able to counter the advances of the other as both were using logic.  The Daleks returned to Skaro to find Davros to see if he could give them an advantage.  The Movellans tried to get the Doctor to give them the same advantage.
In the 2000AD series Rogue Trooper, the North (Norts) and South (Southers) of the Planet Nu-Earth, for hundreds of years, have been in a perpetual state of war against each other using conventional, biological, chemical, and nuclear weapons. The length of the war as well as the weapons involved have turned the planet uninhabitable without protective suits. It was for this reason that the Southers created the GIs or Genetic Infantry which would be able to survive in the environment.
Joe Haldeman's The Forever War is about a war that is made perpetual due to the Einsteinian time dilation effects due to space travel. The novel is said to have been shaped by Haldeman's experience in the Vietnam War as the book contains references to the war paired up with sci-fi concepts. A quote by Haldeman shows great influence from Hobbes' concept of perpetual war, "Life begins in a bloody mess and sometimes it ends the same way, and only odd people seek out blood between those times, maybe crazy people."
In the original Star Trek episode "A Taste of Armageddon", the neighboring planets of Eminiar and Vendikar have been at war for 500 years. To avoid the physical devastation of an actual war, the belligerents agreed to conduct only computer-simulated attacks as long as the resulting "victims" voluntarily kill themselves in "disintegration stations".
The 2006 film Children of Men displays themes of perpetual war by exploring the wars on Terror and Poverty. The movie is set in a dystopia suffering universal infertility. The social and political world has become chaotic as few people exercise social power from their wealthy positions. Meanwhile, there is constant conflict all around the world, which specifically the oppressed group suffers. Manohla Dargis of The New York Times takes notice to the norm of bombs casually exploding in public places, such as a cafe. Dargis writes, "It imagines the unthinkable: What if instead of containing Iraq, the world has become Iraq, a universal battleground of military control, security zones, refugee camps and warring tribal identities?"

See also: Arab–Israeli conflict
Endemic warfare
Just war
List of ongoing armed conflicts
List of wars extended by diplomatic irregularity
Permanent war economy
Perpetual peace
Rogue state
Roman–Persian Wars, noted for being "never-ending" by classical authors
Si vis pacem, para bellum
Syrian civil war
The Report from Iron Mountain
War as metaphor
War Is a Racket

Notes: 

References: Perpetual War for Perpetual Peace, by Gore Vidal. Nation Books, 2002. ISBN 1-56025-405-X
Perpetual War for Perpetual Peace, edited by Harry Elmer Barnes, The Caxton Printers Ltd., 1953 -  Perpetual War for Perpetual Peace

External links: Homeland Security: When The Phoenix Comes Home To Roost, by Douglas Valentine.
The Eternal War Parade, from Intervention Magazine.
The State, by Randolph Bourne – origin of the phrase, "war is the health of the state".
The War on Drugs as the Health of the State, by Bob Black.
The Doctrine of Armed Exceptionalism. by William Hartung.