The I and II world wars are 25 years apart, which is within the length of one generation. This is interesting, because it creates a premise for an entire part of a generation to be both without fathers and grandfathers. Have there been other wars separated by the length of one generation (20-30 years)?
In the U.S., the French and Indian War, 1754-1763 was about one generation ahead of the American Revolution 1776-1783. If you take the Texas Revolution of 1836 as the "start" of the Mexican-American War, the 1836 start was 25 years ahead the Civil War (1861-65).
The argument is that the earlier wars "incubated" the later wars, as some historians believe was the case with World War I and II. The French and Indian War caused the taxation (and set up a potential alliance with France), that led to the American Revolution. And the wars of Texas and America against Mexico sharpened the slavery issue, helping to incubate the Civil War.
The "third wars" in these sequences were the War of 1812 after the American Revolution, and the Korean War after World War II. There was no "third war" after the Civil War because of the exhaustion of the Americans.
There were plenty: E.g. the Austro-Prussian War (1866) and the Franco-Prussian War (1870–1871) form such a pair. Obviously Prussia (soon to become center of the German Empire as proclaimed by Wilhelm I in 1871) participated in both.
As a European who has been born in the 1960s I rather often comment to my friends that it has been extraordinary good fortune for us members of an generation that hasn't had to witness war (from up-close) during their lifetimes (keeping fingers crossed.) I give credit partly to the shocks of the two WWs (on the destructive side) and the developments leading up to the founding of the EU (on the constructive side) each.
UPDATE: I now realize that I have answered a slightly different question by mistake, i.e. one for pairs of wars with a time span of 25 years or less (sic!) in between. Sorry for that.
How about the Punic Wars? The first war was 264 to 241 BC. The second was 218 to 201 and the third 149 to 146. There were 23 years between the first two and 52 between the last two.
What about three generations in a row?
From the series of Polish-Teutonic Wars that took place between 14th and 16th century, I would refer to three periods of time. 1409-11 (with the Battle of Grunwald, which was one of the largest military engagements of medieval Europe) during the rules of Władysław II Jogaila, then a generation later, 1431-35, at the end of his reigns, and finally another generation later, Thirteen Years War (1454-66), in the times of Casimir IV Jagiellon.
The French Revolution begun in 1789 and the Battle of Waterloo was 1815, 25 years later. I think you could also find many examples during Hundred-Years War.
Also crusades can be set in 10-30 year steps:
- 2nd (1150)
- 3rd (1190)
- 4th (1202)
- children's (1212)
- 5th (1220)
- 6th (1230)
- 7th (1250)
- 8th (1270)
(dates rounded, full list eg. in Wikipedia)
The French Revolution (begun in 1789) happened around a decade before the Napoleonic Wars (late 1700s-1814). That's a clear case, too, of the one leading to the other, as the instability surrounding the Reign of Terror and so on led directly to Napoleon gaining power in France.
One could argue that there's a similar link between the Russo-Japanese War of the early 1900s and the Great War, as it demonstrated that Russia was weak and could be taken. As with the French Revolution / Napoleonic campaigns, though, that might be too close for you, as you had more or less the same cohort fighting in each instance.
My other example was going to be the Punic Wars, although those too have already been mentioned. If ever one conflict led to another...