No one has ever used a nuclear missile, either submarine or ground based, in anything other than a test.
Air to air combat, colloquially called dog fighting, has become so rare in the post-World War II era that there is not a single fighter ace (i.e. a pilot with five kills) flying today. Only about three U.S. pilots have shot down even three enemy planes each in the last decade and a half. One estimate, trimmed to include only post-World War II conflicts is as follows:
Canada 2 (additions to WWII scores)
North Korea 2
PRV 16 (17?)
Amphibious assaults have likewise been rare in the post-World War II era:
During the Korean War the U.S. Marine Corps landed at Inchon. . . this battle eventually resulted in intervention by Chinese forces on behalf of North Korea.
The Royal Marines made first post-WWII amphibious assault during the Suez War of 1956 when they successfully landed at Suez on 6 November.
In the Falklands War, the Royal Marines' 3 Commando Brigade, (augmented by the British Army's Parachute Regiment) landed at Port San Carlos on 21 May 1982.
During the Persian Gulf War, a large amphibious assault force, composed of US Marines and naval support, was positioned off the coast of Kuwait and Saudi Arabia. This force was composed of 40 amphibious assault ships, the largest such force to be assembled since the Battle of Inchon. The object was to fix the six Iraqi divisions deployed along the Kuwaiti coast. Due to early misadventure, the mission for this amphibious force turned into a feint. . . .
The most recent amphibious assault was carried out by the Royal Marines when they landed at the Al-Faw Peninsula on 20 March 2003 during the Iraqi War.
Wikipedia briefly sums up post-World War II Naval warfare history:
Three major naval conflicts took place in the second half of the 20th century, of which two pitted fleet against fleet.
One was the well known Falklands War, pitting Argentina against the United Kingdom. The Falklands in particular showed the horrible vulnerability of modern ships to sea-skimming missiles like the Exocet. One hit from an Exocet sank HMS Sheffield, a modern anti-air warfare destroyer. Important lessons about ship design, damage control and ship construction materials were learnt from the conflict.
The other took place 11 years earlier in 1971. It was the third and last of the Indo-Pakistani Wars, in which Bangladesh gained independence from Pakistan with Indian assistance.
The third major naval war took place between Iran and Iraq from 1980 to 1988. It did not feature any large fleet battles, but it featured attacks on merchant ships as routine for the first time since 1945. It also featured the largest surface action since WWII, when United States Navy ships went after Iranian oil rigs to punish the Iranians for their actions in the war. Iranian naval vessels intervened, and Operation Praying Mantis resulted.
At the present time, large naval wars seem to be very rare affairs, with the main function of the modern navy being to exploit its control of the seaways to project power ashore. Power projection has been the primary naval feature of conflicts like the Korean War, Suez Crisis, Vietnam War, Konfrontasi, Gulf War, Kosovo War and both campaigns of the War on Terrorism in Afghanistan and Iraq.
Tanks haven't vanished from the military scene, but the tank on tank battles envisioned by Cold War planners haven't materialized to the extent expected. Infantry with anti-tank weapons and road bombs have been the biggest threat to Israeli and American tanks. Aircraft, helicopters and anti-tank missiles on Bradley fighting vehicles were all comparable in importance as anti-tank missiles to American tanks in the Iraq War.
It isn't that the last 62 years have been peaceful. There have been at least a hundred wars at any given time for the majority of that time period, but most have been civil wars/insurgencies overwhelmingly fought on the ground with relatively light weapons. There have also been a fair number of major air bombing campaigns in that time period. And, the last 62 years have also seen dramatic changes in technology.
I am not trying to make the point that these weapons systems or modes of military combat are irrelevant to modern military planning, although some may be. Instead, the main point is that a very large share of military procurement budget is spent on weapons systems and combat modes that have never been thoroughly tested in modern warfare. War games have been the sole real test of a great many of them. And, real warfare almost always brings surprises.
The Iraq War and Afghan War caught the U.S. with too few people with Middle Eastern language skills, too few light armored patrol vehicles, too little body armor, too little counterinsurgency training, insufficient protections for tank gunners, and surprisingly poor performances by Apache attack helicopters. On the other hand, it has rejuvenited support for the B-52 and A-10 military aircraft, which turned out to be more useful than anticipated. Difficulties associated with convoy operations in these recent wars have also spurred development of a light cargo aircraft for the Army, and have greatly boosted the use of drone aircraft. These wars have also pointedly shown the importance of long term planning in military operations -- both were wildly successful early on, but have shown that capitalizing on early military victories in an asymetric conflict isn't easy.
The sheer number of lessons learned by U.S. troops in these recent conflicts is particularly notable because the wars the U.S. has joined in Iraq and Afghanistan are the kind of conflicts that the world has had a great deal of experience with since World War II. Both countries have hosted prolonged ground wars themselves prior to U.S. involvement. The U.S. fought in Vietnam. And, there have been a great many insurgencies, especially in the post-colonial area.
If U.S. troops had to make this big of an adjustment to the lessons of historically well precedented ground warfare, how much more do we have to learn when and if naval warfare or aerial warfare or worse yet, nuclear warfare, breaks out? There are simply so many imponderable points that no one can credibly predict how events would actually play out in a major conflict of these types. Subtle limitations imposed by the quirks of rules in a war game, and simply a failure of ingenuity on the part of participants whose lives aren't on the line, can profoundly change real world outcomes. In times of peace, no military planner is really reality based.
It is hard to tell from isolated small incidents, like the Falklands War, or an F-117 shot down over Serbia, how much of the outcome was a fluke and how much represents a systemic problem with U.S. military planning. One can learn the wrong lessons from an event, and if everyone learns the wrong lessons, the experience can actually be counterproductive.
We prepare in the hope that we will never have to put our preparations into action, but the longer we go without using modes of warfare in real life, the less anyone can be confident that we are actually prepared.