During the First World War, Nestor Makhno, the great Ukrainian anarchist revolutionary, returned to Ukraine after being released from prison to discover that the Soviets had signed Ukraine away to the Germans. With just 30 men and one Maxim machine gun, he crept into a nearby town under cover of darkness where a thousand German troops were bivouacked in the town square and proceeded to massacre the entire German force while they slept. The few German soldiers who escaped were hunted down by angry townspeople with gardening implements and killed. Makhno's anarchist army — the Makhnovshchina — was never larger than 50,000 men, had no training, and whose sole source of equipment was captured enemy supplies, managed in the end to drive off 600,000 professionally-trained German soldiers.
Battle of Lepanto. Those fat, rich, decadent, wussy, Venetian wimps. Should be lots of fun to pick on, right? In the first two battles the Venetians lost. In the third and best-known one, in 1571... they got dangerous. Very dangerous. There was intervention, naval combat experience and bucket-loads of money from multiple sources, mainly Spain. The Venetian Galleasses and their mixed crews were said to have accounted most of the Ottoman galleys sunk. Galleasses were the first ships able to deliver a broadside, while galleys could only fire from the beak of the ship.
Rukhsana Kauser. An Indian peasant girl in Kashmir. When some terrorists came by her house to forage, she killed an internationally wanted terrorist leader. In close combat. While outnumbered and outgunned. To protect her parents. At age 18. With a hatchet.
World War One was this for Canada, in terms of international reputation. Before WWI, they were some obscure backwater colony. By the end of the war, the Germans knew in no uncertain terms that they were in for hell if the Canadians attacked them.
A similar situation occurred for Australia. A famous quote on the matter was that Australians were "lions led by asses" (the asses being the British Commanders), and the Turks consider Australia to be a Worthy Opponent.
It should be noted that 'lions led by donkeys' was a term directed at the entire British and Dominion force, it applied just as much to British troops on the Western Front as to Australian troops led by British officers at Gallipoli (and popular history distorts this as well, as many of the leaders at Gallipoli deemed incompetent were actually Australian). It was a statement also shown later to have been completely fabricated by a historian on the winning side with an animus against the British.
The war also features the rise of the United States in the circle of the great powers. Before the war, their military was considered a joke (leading to Spain's complete loss of face when they were crushed in the Spanish-American War). Then the US Army started deploying ten thousand soldiers per day with their support equipment and weapons, US industry supplied the allies with weapons and other equipment (in particular, this is the time when Italy's chronic shortage of machine guns ended thanks to American supplies), and they weren't fully mobilized yet.
At some point in every nation's history, they were not looked on as a military power. For every nation that ever became one, there was one of these moments.
The Battle of Cannae during the Second Punic War for Rome, even though this particular example is better known as a Crowning Moment Of Awesome for Carthage. When the Carthaginian army had the Romans surrounded and were cutting them to pieces, the remaining soldiers, under the leadership of Scipio Africanus, decided they weren't going to get slaughtered by Hannibal, and hacked their way right through enemy lines and to freedom. They ended up being The Scrappy of the Roman military, but were Rescued from the Scrappy Heap when Scipio used them in his army that crushed Hannibal at Zama.
This incident is rather exaggerated. Scipio Africanus was at Cannae but did not have a position of command and the 'remaining soldiers' were at least a legion strength, if not as much as 14,000 men, depending on the source, who cut their way out. What is a Lets Get Dangerous moment is that, supposedly, after the battle of Cannae, when Scipio heard that some people were calling for surrender, took some of his friends and marched into the Senate (which he would not have been allowed to enter because of his youth) and demanded that they not surrender, although most Senators were in agreement. He also is said to have charged the Carthaginian lines at the battle of Ticinus to save his father. Pretty much all of this is from Polybius, who was a client of Africanus' grandson (by adoption) Scipio Aemilianus, and is generally regarded to have exaggerated (although probably not outright lied about) things with regards to that family.
Adolf Hitler is a perfect example. He was a near homeless vagabond until he got into the army. After discharge and a period in prison, he quickly rose, managing to become Führer with only a few setbacks and with a grand total of six initial allies and an impressive ability to make speeches. He took the title of Fuhrer after he seized power and combined his current position with that of Chancellor. He went from being a dropped-out painting student to being leader of a nation.note The title of Fuhrer went back to the tribes in Roman times. The title 'dux' was then, in the 19th century, translated to 'Führer', as 'Führer of somesuch people'. Same for Hitler; 'Reichskanzler Adolf Hitler, Führer des Großdeutschen Reiches'. Führer amounted to little more than a ceremonial title since there never was the position of 'Führer'.
Vladimir Lenin is an even better example. He came out of exile and took down a government, after spending decades doing nothing much (unless one counts plotting).
Stalin's rise was also impressive. A minimally educated legal secretary who took over his entire government.
Likewise Mao Zedong, who was a librarian when he engineered the takeover of the Chinese Communist Party.
For a nation who aren't exactly the first to come to mind when you think of military powerhouses, The Winter War is something of an eye opener. With 1/3 of the troops, 1/30 of the aircraft, and somewhere between 1/100 and 1/200 of the tanks, they sure gave the Soviets some wounds to lick.
Simo Häyhä, or "The White Death", was an ordinary farmer who was, naturally, called up to help with the Winter War. He now has the record for the largest number of confirmed kills ever. He got so dangerous the Russians started operations specifically to kill him, starting with patrols where he was known to be, then escalating to snipers, countersnipers, and shelling the woods he was hiding in.
Not only that, but they got lucky and put him in a coma for nine days when one of those artillery strikes got close enough. The Soviets stopped advancing and ended the war the same day that he woke up. Some like to think they heard the White Death had come out of his coma and was about to drive them out, and they quit while they were ahead.
It wasn't even artillery fire that took him down (the worst that ever did to him was rip up his jacket one time). He got taken down by a Soviet counter-sniper who managed to shoot him in the face. He then got back up, killed the counter-sniper (who was the last survivor of his team), and was hiking back to base when he met a friendly patrol and passed out. The patrol thought he was dead.
Finnish Air Force. Its final kill-to-loss tally, losses of bombers included, was 5:1. There are more Finnish fighter aces per capita than in any other air force. The two highest scoring non-German fighter aces, whose tally can be verified, are Finns.
Croatia. It is a relatively small state, with only 4 million inhabitants, but consider this:
It fought for 300 years against the Ottoman Empire. Around 80 years with virtually no help. For comparison, Serbia became an Ottoman province after 2 battles, and many other states (Bosnia, for example) did not fare much better. All while fighting among themselves. Ottoman Turkey, the grandest empire of its era, never gained a foothold in Croatia.
3 wars against Bulgaria, which was (at the time) several times larger in territory. First two ended in stalemate.
Battle of the Bosnian Highlands between Croatian forces under future King Tomislav and Bulgarian forces under Alogobotur.
30-year-war. Entire separate type of light cavalry was named after them. They were also used as raiders, so much that there is still a prayer in one German church which asks God to save people from plague and Croats. Some accounts even maintained that the Swedish king was killed by Croats, although that was disproved — the king was killed by Imperial Gotz curassiers.
The Croatians also fought on both sides of World War II, forming one elite division of the German Army, one complete Waffen SS division, one part of a Waffen SS division, as well as starting first organized resistance movement against German occupation.
Yugoslav wars. In 1991, when fighting started, the most numerous, best trained, and best equipped Croatian military units were not military at all, but rather Special Police forces. The Croatian National Guard was formed in 1991 and gradually developed into a full-fledged army by 1993.
The United States after Pearl Harbor was bombed. The Japanese had estimated that it could successfully win a war against the U.S. since both of their military's production output was roughly equal. The problem was, the U.S. wasn't in a war yet, and so its production of war material was only so-so, while the Japanese had been fighting a war for nearly ten years, and were going flat out. Suddenly, an entire nation wakes up and bears its wrath upon Japan. Eventually, the U.S. was building ships faster than the Japanese could sink them. Everything new and great was first sent to Europe, and the USMC was effectively dead last on the supply chain for everything. Hell, the Marines didn't get to use the Garand until after the National Guard and Marines used the bolt action Springfield 1903 for the entire war!
Let's not even get started on the atomic bomb.... (although, one may think of this as a case of good fortune for them).
Firstly, Yamamoto knew the Americans would flatten them in the long run (ie, at best he figured they'd get about 1 year of victories), secondly, Lend-Lease had been in effect for 9 months, so they were already spooling up their industrial strength.
Basically the same thing happened with Russia, it heavily counted toward winning the European war. Namely, after losing the Winter War noted above, Hitler decided that the Soviet Union was too pathetic to keep as allies, and decided to turn on them. What Hitler didn't realize was that the reason the Russians lost that war was poor planning, supplies, and a truly badass sniper. So what happened after the Soviets' recovered from the initial string of many German victories? They bled out the bulk of the German army's best troops in the meatgrinder that was Stalingrad, crippling the German war machine long before the USA got involved. Then they eventually went on the counteroffensive and crushed every last German force and stronghold between Moscow and Berlin, even managing to beat the Western Allies to the German capital. There is a very good reason why Make the Bear Angry Again is a trope, and why there is an "again" in its name.
Ancient Greece. What happens when Persia, one of the world's greatest powers, attacks a ragtag band of city-states that fight each other more passionately than they do anything else? Said superpower gets owned in a series of wars with said ragtag band of infighting city-states, that's what happens.
The Battle of Britain. Outmanned and outgunned, Britain faced the might of the Nazi war machine alone, having seen the BEF get curbstomped in France. With the help of radar, the RAF utterly tore apart the Luftwaffe, with resistance pilots such as the terrifying 303rd squadron from Poland.
Mind you, Poland, well, just look at the stats for the invasion; half as many troops again, twice as many artillery pieces, 3 times as many tanks, and almost 6 times as many aircraft, and all of it better than what the Polish had, and it still took the Nazis 5 weeks, and the Soviets coming in from the other side (with half as many troops as the Poles started out with, but massively outnumbering them in every other way). In 6 weeks the next year, the Germans had overrun the Netherlands, Belgium, France, and Luxembourg (and with backup from the British), a combination which altogether had numerical parity in troops, more tanks and guns, a much slimmer disparity of aircraft, and overall much more modern equipment.
Mexico: Mexico was just starting to come back from losing over half of its former territory to the United States when Napoleon III decided that he wanted a state under French control in the Americas. Mexican president Benito Juarez had stopped paying foreign debt to France, Britain, and Spain, and this was used as an excuse by the French to launch an invasion. The then best army in the entire world was defeated by an inferior army in both training and equipment (not to mention numbers). Even after the French achieved victory and installed their own ruler, they were forced to leave the country by the constant Mexican attacks.
The Texas Revolutionaries against Mexico. Two massacres at the Alamo and Goliad left them decimated and the United States pulling their support. They were chased to the brink at San Jacinto with Santa Anna prepared to finish them off on April 22, 1845 (even with Santa Anna diverting many of his troops, they still outnumbered the Texians more than 2 to 1). So all Sam Houston decided to do was engage the fight a day early — taking advantage of Santa Anna's incredibly stupid decision to not post lookouts — and took the sleeping Mexican army by surprise. Despite greatly outnumbering them, the Mexicans surrendered in less than 20 minutes, with Santa Anna, the President of Mexico, being taken prisoner by the Texians.
Erwin Rommel, who led a combined Italian-German force in Africa, had a good opinion of the Italian soldiers but a horrible one of their officers, and is quoted to have said of them "Good soldiers, bad officers; however, don't forget that without them we would not have any Civilization" (The Rommel Papers) and "The German soldier has impressed the world, however the Italian Bersagliere soldier has impressed the German soldier" (the Italians placed the latter phrase on a plaque at their military graveyard near El Alamein).