The Peloponnesian War lasted over two dozen years (431–404 BC). Think of it as being something akin to the Cold War (the modern one between USA and Russia) where it is mostly political maneuvering and proxy wars. However unlike the Cold War, direct and intense fighting between the two biggest warring states (Sparta and Athens) did also break out with multiple cities being captured or destroyed. But there would also be times of relative peace after armistices or peace treaties were signed. However, the peace treaties were not enough to stop the conflict from continuing, if they were ever intended to. For instance, the Peace of Nicias, at the time called the "Fifty-Year Peace" was intended to last 50 years. It lasted about 5 years. The Athenians' main goal of the treaty was to have Amphipolis returned to their control, but that was negotiated out of the treaty. So it was pretty much determined that the fighting would definitely resume and the Fifty-Year peace was just an indefinite armistice.

You might ask, five years is a long time, shouldn't that be called a different war, then? Yes and no. The two phases of the war between the Peace of Nicias are called the Archidamian War and the Ionian War. However because it is essentially the same conflict with mostly the same parties involved, fighting for the same reasons, it is all considered one war even though there were long periods of relative peace. When it comes to two major expansionist powers that are close to each other, it is often just a matter of perspective as to when one war has ended and another has begun. Some historians would say that WW1 and WW2 were really just one long war and it is possible that future historians will give them just one name which everyone will commonly refer to them by. This is called periodization: picking a start and end point for a given series of events in order to facilitate study and discussion. You can't really study The Ionian War without also studying the Archidamian War. Thus we have the Peloponessian War.

So you have something like The Hundred Years' War, which you probably had in mind when you asked this question, which could also be considered three separate wars: The Edwardian Era War (1337-1360), the Caroline War (1369–1389), and the Lancastrian War (1415–1453). So The Hundred Years' War is "war that lasted 116 years" but during that time there was 35 years of truce.

Generally, such "wars" are a sequence of conflicts spread out over a long period where each individual conflict does not resolve the overall state of hostility between the opponents. They would specifically not be one long ongoing "war" with battle occurring constantly for a series of years.

Some modern examples might include the WWI + WWII series of wars, or the Cold War. One could easily consider the two World Wars as part of a larger conflict, and if they had happened farther back in the past it's likely there would be more historians arguing they be treated that way. As for the Cold War, there were several "hot" wars during it (Korea, Vietnam, Afghanistan, lots of smaller wars without direct involvement of a major power, etc.) over a period of nearly half a century.

Going back farther, there are many similar examples. In the Napoleonic wars you have multiple different campaigns over the course of a decade. But each one was in itself not that long and the overall conflict can be broken up into about 6 or 7 different individual wars, combined with the overall conflict between France and Britain (which normally didn't involve full-scale armed conflict between the two powers). You have the hundred years war, which saw individual conflicts intermixed with periods of stalemate or hostile but mostly passive co-existence and periods of peace.

A good modern example would be the Arab/Israeli conflict, which has persisted for over 60 years. At no point in the ongoing conflict was one side or the other defeated to the point of losing their sovereignty. Every war has resolved in a way that has left the belligerents in a condition to continue the conflict in the future and retain their hostilities toward one another. That's what an extended war typically looks like. A series of battles or even a series of wars over a long period of time, where none of the individual battles resolves the underlying conflict or results in a change of the conditions which allow the conflict to continue.