I have an incredibly generalized and glossing overview of this subject here that you may be interested in. However this post does not answer your question at all.

There are five main candidates and it depends entirely on your perspective. Some would say the American Civil War was the last true attempt at application of the "Napoleonic style of war" with dense "column" formations and battalion level organization and so forth. I go into some of the issues with the war and classifying them as "Napoleonic" in this post if you're interested. Some would say the Austro-Prussian War in 1866 where the Prussian breech loaded rifles went up against the Austrian muzzle loaded rifled muskets or the Franco-Prussian War where both sides used "dense" formations which, to an unkeen eye, seem similar to Napoleonic tactics. Finally, some would say that the Crimean War in 1853 or the Italian War in 1859 as the former was the first war to see the use of rifles en masse and the latter the first to see both sides using rifles. All of these are correct and so are none of them.

In terms of operations/strategy though I'd argue the Napoleonic "style of war" never died out. Jomini^[1] defined the the "old style" of warfare with having limited armies and limited combat with *"armies in tents, with their supplies at hand, engaged in watching each other."*^[2] Armies were basically kept in large mass together and thus relied on major supply trains, depots, and complex administrative systems to supply them and, as Jomini says again, kept them on a "short leash". Napoleon changed that forever. By allowing them to feed off the land these armies could move faster and by breaking them up it was near impossible for the enemy to ascertain their objective (as opposed to one giant, slow moving mass) which caused them to be overrun. Napoleon's *"insistence on speed and mobility was a basic feature of the Emperor's campaigns from beginning to end, and was the feature of his warfare that most confused and unsettled the majority of his opponents, brought up in a tradition that taught a more leisurely type of warfare."*^[3]

/u/DonaldFDraper always likes to tell me how in many ways Napoleon was an unoriginal tactician but his brilliance came from his organization and administrative changes. That he did not win those spectacular victories because of some tactical, battlefield level change but because of his corps system and his great administrative talent. Napoleonic warfare was not just column formations and cavalry charges and musket volleys; it was a fundamental rearrangement of how war was fought. Napoleon brought something that lacked throughout the entirety of the 18th century -- decisiveness. He could force the engagement. He could be hyper aggressive and force the enemy to fight and constantly bash away at them. The Corps d'Armee are, to me, what Napoleonic warfare is all about and the concept of raising the operational level of warfare beyond the Regiment is still in practice to this day.

However those are weasel words because we all know what you meant; you want the tactics. In Europe Napoleonic tactics would get terminally ill in Crimea with the use of the first thin rifle chains and die finally in the Franco-Prussian War. The Franco-Prussian War saw limited uses of trenches, more defensive orientation from the French, massive frontline artillery batteries of modern Krupp Guns, and most importantly it saw the Prussians, in the face of massive casualties, reorganize their infantry into massive skirmisher formations. Where men would stand 2-3 meters apart 70 men wide and 2 rows deep with a "reserve" of 4 more rows behind them to reinforce as necessary; a very First World War style of fighting that would persist into 1918 even. It made them less susceptible to rifle fire but still made them a tight enough body to receive orders via sound and to bolster each others confidence and to act as a single mass. However it was an entirely different style of war by this point we can definitively say.

For America however, and this is the nuanced part, the American Civil War would be the answer to me. As I mention in the linked post above the Civil War was America's first real experience with modern warfare. Their last war with a European power was 1812, something I'd still certainly classify as Napoleonic at least in title, and everything up to that was a more guerrilla styled of war with Indians. Even the Mexican-American War saw an incredibly limited size of armies with the largest army fielded being only 12,000 men by General Scott. The Civil War was literally a case of Napoleonic tactics being applied to a modern battlefield. As I, again, mention in my post and I wont' go into depth here as it would just be redundant it was not really Napoleonic tactics but it was the attempt of application of them so I feel it's a fair assessment. That would certainly be the death of it for the American sphere.

TL;DR:

1. I'd say the operational and strategic level of war of the Napoleonic Era never died but is the foundation of which modern and even contemporary warfare is be built upon. The Corps system changed war forever and remains in some manifestations to this day.

2. The Crimean War saw the first use of rifles used en masse and the Franco-Prussian War saw the beginnings of loose WWI-esque formations along with trenches and massive artillery batteries. I'd say these two wars spell the end of Napoleonic war in the Western world with one exception.

3. America, the exception, would have its drift away just 5-9 years prior to the Franco-Prussian War with their own Civil War which was a far more applied case of Napoleonic tactics being used (or, at least, the attempt to do so).

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Notes:

^[1] Jomini was a 19th century military thinker. Think a contemporary of Clausewitz but a Swiss who studied the French. His work would be the central understanding of warfare for the American war colleges prior to the Civil War.

^[2] Antoine Henri Jomini, The Art of War, p.123

^[3] David Chandler, The Campaigns of Napoleon, p.148

David Chandler, The Campaigns of Napoleon

John Elting, Swords Around a Throne: Napoleon's Grand Armee

Michael Howard, The Franco-Prussian War: The German Invasion of France