The war with the Dire Wraiths starts out this way in ROM: Spaceknight.
The Swedish cyberpunk comic De osynliga kriget turns out to be about a war fought with nanotech robots - destroying factories and infrastructure by making buildings fall down. To the public, that's just sloppy building practices that are part of their already Crapsack World.
Fan Fiction
Fittingly enough, a Secret War is what a 40k fanfiction called Secret War is all about.
Film
The war between vampires and lycans in the Underworld series.
Partly thanks to the Cleaners, a group made up of elite human soldiers and headed by the first immortal Alexander Corvinus. Their job is to work behind the scenes to clean up the mess the immortals leave behind.
Also, the war between vampires and one very angry half-vampire in Blade
Blade: You better wake up. The world you live in is just a sugar-coated topping! There is another world beneath it - the real world. And if you wanna survive it, you better learn to *pull the trigger!*
The Resistance of Zion vs. the Machines inside The Matrix.
In Hellboy, it's mentioned in passing that World War II was simply the public front of the Occult War, which only came to an end with Adolf Hitler's real death in 1958.
Literature
The long conflict between the Dark and the Light in The Dark Is Rising series.
The war between the Muineers and the mutineer-Mutineers in the first Empire From The Ashes book, which has been going on since the dawn of human civilization. By the end of the book, it has become very, very not secret—people don't know what the hell is going on, but they sure can see the mayhem.
Fyodor Berezin's The Lunar Option describes battles on the Moon between the American astronauts and the Soviet cosmonauts during the 60s, after the discovery of an alien artifact. Obviously, no one in the general public is aware of this.
Several of these in The Dresden Files, primarily among them the war between the White Council of Wizards and the Vampire Courts. There's also an even more secret war known as the Oblivion War, whereby a secret brotherhood known as the Venatori wage a conflict in order to eliminate all knowledge of certain monstrous entities, as knowledge of them possessed by mortals connects the entities to the real world.
The various Weird Wars in the Diogenes Club stories by Kim Newman. Every so often an evil Great Enchanter arises, and it's the Club's job to put him down again.
If won, it would only be written of in the secret histories. If lost, there would be no more histories, secret or otherwise.
The war against the Yeerks in Animorphs. Until everything gets blown wide open in the end of the series.
The conflict between Light and Dark Others in Lukyanenko's Night Watch. Although it has become more of a cold war with the occasional black operation or two after the treaty that established both Watches and the Inquisition.
Live Action TV
In the Stargate Verse the US is involved in interstellar conflicts, and doesn't even tell the heads of other nations at first, never mind the world at large.
A number of the UNIT stories in Doctor Who work this way, particularly in the classic series.
In the War of the Worlds series, only a handful of military, intelligence and science personnel know about the alien invasion coming out of dormancy. In the second series, the new aliens appear more human and are able to operate openly, since it's become such a Crapsack World that to most people they're indistinguishable from the corrupt corporations and organized crime.
Alphas has the fight between the alpha terrorist organization Red Flag and the Department of Defense and their own alpha team. In the first season finale Rosen breaks the masquerade, realizing that this secrecy ensures conflict where it might be avoided, facilitates atrocities on both sides, and is exactly what the Big Bad alpha Stanton Parish wants.
Old World Of Darkness is rife with secret war, going down between virtually every species of supernatural being, between different factions within the same species, and between supernaturals in general and those few groups of mortals who have been clued in to their existence.
Nephilim. The eons old combat between the title characters and the secret societies hunting them.
Call Of Cthulhu supplement Glozel Est Authentique, adventure "Secrets of the Kremlin''. The Nodens Brotherhood has long opposed a cult that worships Shub-Niggurath.
On the subject of Call of Cthulhu, the entire Delta Green third-party supplement. Delta Green versus MJ-12, with a second front against the Karotechia (who occasionally also conflicts with MJ-12) and the odd fight or two against a random Mythos cult.
Bureau 13, AKA Stalking the Night Fantastic. The title Bureau fights against supernatural monsters.
Chill. S.A.V.E. (Societas Albae Viae Eterniata AKA The Eternal Society of the White Way) does battle with supernatural creatures from The Unknown.
Feng Shui has a secret war that spans at least four different junctures in time, along with the Netherworld that connects these junctures, each with their own different factions vying for the power to remake human history in their image.
The game Conspiracy X also has a secret war involving reptilian aliens and other weirdness.
The Shadowrun universe has rival Mega Corps waging a covert war against each other, with the titular Shadowrunners being the deniable assets that the corps call upon to do their dirty work.
GURPS Black Ops. The PCs all work for "The Company", a secret organization with the twin objectives of 1) Kill all the aliens/psis/monsters trying to take over and 2) Don't let anyone outside The Company find out about the aliens/psis/monsters trying to take over.
The Infinite Worlds default setting has the two factions of Centrum and the Infinity Patrol who oppose each other at every turn and vie for control and influence on low-tech worlds, all while trying not to be detected by the natives of that timeline and expose their own existence.
Cthulhutech gets crazy with the strength of their Extra Strength Masquerade. The shadow war between the Eldritch Society and the Chrysalis Corporation taking place within the arcologies and suburbs of the NEG-controlled areas is one thing, and the Chrysalis Corporation are very good at keeping things under wraps and discrediting or eating anyone who knows too much and might actually expose anything (plus, they have the leverage to have the government censor Dhohanoid-related reporting to prevent public panic). However, not only are Eldritch Abomination cults are alive and well, but one has formed a military force that has conquered China, under wraps, and the fact that the last Aeon War is still going on and the Migou are attacking again with a force equal to the one that nearly took Earth apart the last time. And the NEG can recruit people to fight on the China front without them knowing a thing about the war until they're already in too deep to back out.
In Unknown Armies this is the default state of the Occult Underground. Being composed of very driven, obsessed and, a lot of times, outright insane people, the Underground in most cities is either in constant conflict between the different cabals, or is just at the tipping point of an all out war.
Video Games
In the Assassin's Creed series, there is an ongoing, secret war between the Assassins and the Templars, which has been waged since the beginning of the human species, ever since humanity first rebelled against Those Who Came Before.
The war between the Forgotten and Abaddon's forces in Guild Wars: Nightfall qualifies. The Forgotten have spent the last thousand years fighting a slowly-losing war to keep Abaddon and his followers bound in the Realm of Torment. As of present, they maintain only scattered outposts in either dimension.
The Order of Whispers was founded to pursue such conflicts. They have watched over Palawa Joko's tomb, kept the existence of Abaddon and his demons from public knowledge, and a century before the game even interrogated and imprisoned a Titan.
Callof Duty Black Ops takes place entirely from the perspective of SOG operatives during the Cold War, predominantly in Vietnam. In addition to taking part in openly historic events like the Tet Offensive, the player attempts to assassinate Fidel Castro, sabotage a Soviet space program, and uncover the truth behind a brainwashing scheme that he himself is victim to. The game even emphasizes its covert overtones by redacting the character, location, and date information displayed at the beginning of every mission.
Its Callof Duty Black Ops 2 sequel continues this trope before subverting it. Flashback missions show the previous game's protagonist unofficially fighting in African civil wars and deposing/supporting foreign dictators, but his son, a Navy SEAL, fights off a VERY visible unmanned drone attack against Los Angeles thirty years later.
As the name implies Deus Ex Invisible War focuses on a shadowy conflict between several clandestine groups over the future of humanity. The player can end up siding with any faction or even Kill Em All.
In Avatar The Last Airbender, the war is secret to the Earth King only. The Dai Li took pains to make sure it stayed that way to keep the people of Ba Sing Se from going into a panic and to limit the capital's involvement with the war that would screw up their way of living.
Its hinted that while the Earth King is kept from knowing to make him a puppet, that many of the rest of the citizens don't know either. Brainwashing and control of information keep knowledge down, and constant fear makes those who do know too afraid to talk.
Real Life
Real Life: CIA vs. KGB, CIA vs. Al-Qaeda, etc. The public only knows a very little about what really goes on behind the scenes.
During the Vietnam War the CIA had a whole lot of things going on, including the Phoenix Program: a program of infiltration, capture, terrorism, and assassination).
