I don’t know if the battle of Thermopylae counts - on the one hand Xerxes had anywhere from 150,000 to 3 million soldiers, depending on who you ask. But on the other, the defensive forces were very small - 300 Spartans plus about 700 others. They held the Persians off long enough, and inflicted enough casualties, to allow the Greeks to set up a naval blockade and then heavily damage the Persian fleet, eventually forcing Xerxes to retreat from Greece, changing rhe entire course of the world.
300 + ~7,000. Assuming you believe the notoriously innumerate and somewhat varying sources.
If you count it as a tiny battle, the alleged wrangle between Russian generals Samsonov and Rennenkampf on a train platform before WWI is supposed to have led to lasting enmity between them, preventing them from coordinating an invasion of East Prussia in 1914 which led to the obliteration of Samsonov’s Second Army and ensured that the “Russian steamroller” would not bring an early end to the war.
How about the Alamo? We’re all taught that it was a big deal and to remember it. Seems to me that it was pretty significant in the Texan war for independence and its eventual entry into the US.
The Dogger Bank incident Dogger Bank incident - Wikipedia which the Russians believed was a battle against Japanese forces in the English Channel had the potential to be highly consequential. A bit more blundering, and World War I might have started in 1904 with the UK and Imperial Russia on opposite sides. At the time UK/French relations were just starting to be friendly (the Entente Cordial had been signed a few months earlier), so a war between an established ally (Russia) and a new friend would have been awkward for France - and the Kaiser might have exploited the opportunity.
I would say neither is, they both seek political and military patronage from the United States (and in the past, before the fall of the Iron Curtain, the Saudis at some points sought Soviet patronage).
Perhaps I should have been clearer - a super power is one that others seek patronage from AND does not seek patronage from others - the apex predator of international relations, as it were, while lesser powers are those who seek patronage from others even if yet lesser powers are seeking patronage from them.
Definitely an influential battle, but several caveats. This was one of a series of battles over the English throne. And each army involved represented nearly the entire force of its sovereign. Everyone involved knew the high stakes and were betting all-in.
Thermopylae was a failure: the goal was to hold up the Persians for long enough for the various Greek allies to assemble their land forces once the festival of Olympus was over. In the event, Thermopylae was lost after three days, a gross strategic failure which left Athens so exposed it had to be abandoned to the enemy. Worse, it nearly fractured the alliance as the Peloponnesians began to construct a wall across the Isthmus in order to preserve their own lands at the expense of everyone else. Had it not been for the victory at Salamis, (to which the Greek navy sailed as a hasty fallback in the wake of Leonidas’ failure) the alliance would almost certainly have fractured in the face of overwhelming odds.
The force with Leonidas was sent forward by the Spartans in advance of their main body, that the sight of them might encourage the allies to fight, and hinder them from going over to the Medes, as it was likely they might have done had they seen that Sparta was backward. They intended presently, when they had celebrated the Carneian festival, which was what now kept them at home, to leave a garrison in Sparta, and hasten in full force to join the army. The rest of the allies also intended to act similarly; for it happened that the Olympic festival fell exactly at this same period. None of them looked to see the contest at Thermopylae decided so speedily; wherefore they were content to send forward a mere advanced guard. Such accordingly were the intentions of the allies.
…
As soon as ever news reached the Peloponnese of the death of Leonidas and his companions at Thermopylae, the inhabitants flocked together from the various cities, and encamped at the Isthmus, under the command of Cleombrotus, son of Anaxandridas, and brother of Leonidas. Here their first care was to block up the Scironian Way; after which it was determined in council to build a wall across the Isthmus.
…
For they had looked to see the Peloponnesians drawn up in full force to resist the enemy in Boeotia, but found nothing of what they had expected; nay, they learnt that the Greeks of those parts, only concerning themselves about their own safety, were building a wall across the Isthmus, and intended to guard the Peloponnese, and let the rest of Greece take its chance. These tidings caused them to make the request whereof I spoke, that the combined fleet should anchor at Salamis.
The interesting thing about this thread is that the word small is apparently even more subjective than the word influential.
Well, no one has nominated Stalingrad yet, so I guess that’s something.
Did Stalin send the entire Red Army there? He did not!
Or that little skirmish in Kursk…
I’d say that the Dieppe Raid taught no lessons at all that couldn’t have been absorbed beforehand by reading the various pamphlets published by Combined Operations, and most of the ‘lessons learned’ stuff was rationalisation for the unnecessary scale of loss.
May have been somewhat true of the Normans at Hastings, though we certainly know William hadn’t brought everyone, for example his very important and very richly rewarded supporter Roger de Montgomery who seems to have been left to watch Normandy. But it was definitely not the case with the English (England was quite simply a larger, more populous, wealthier realm). Harold Godwinson seems to have been trying to replicate his surprise attack victory at Stamford Bridge over Harold Hardrada and went basically all in on sprinting towards William’s position as fast as he could with what he had on hand. But William’s army was well-rested as opposed to Hardrada’s force and may have been trying to deliberately draw Godwinson out, raiding in family lands in Sussex. In retrospect Godwinson probably should have waited on the defensive in the vicinity of London to rest and more fully assemble his army. Or let his younger brother Gyrth lead the counter-attack as he had suggested while he gathered a second army.
But he didn’t and as a result we were doomed to this ridiculous hodgepodge of a Germanic, Romance-inflected language 
.
All the crap we anglo-Canadians inflict on the Quebecois? Payback for 1066 goddamit!
That’s because Esperanto-speakers don’t take the step of armed invasion to spread their language. Invade theirs, on the other hand, and you’re in for a lesson in more than linguistics; as Esperantist Ho Chi Minh proved.
I would say that one of the contenders for the OP was the Battle of Quebec, 1775, which if it had gone the other way, could easily have established American dominance over all of North America.
The Americans, in their first invasion of a foreign country, were trying to wrest control of Quebec from Britain. They already held Montreal (Ben Franklin was there with the occupying forces, busy founding the first English language newspaper, the Montreal Gazette, still in operation), while Generals Montgomery and Arnold were trying to capture Quebec City.
However, Montgomery and Arnold had to attack on December 31, in a blinding snow-storm, because many of their troops had only enlisted for a year and could have retreated south the next day. The British and some Quebec militia repulsed the attack. Montgomery was killed in the attack and Arnold started thinking, “Hmmm.”
If the Americans had successfully taken Quebec and Montreal, there’s a real question whether the British could have re-taken the Province in the spring, with their naval power but not much land strength. And if the Province of Quebec remained in American hands, the entire history of North America would have been different. I might be entering this what-if post from the US state of Upper Dakota.
The numbers on either side weren’t very large:
British: 1,800 troops
Casualties: 19 killed and wounded
United States: 1,200 troops
Casualties: 84 killed and wounded; 431 captured
Some Canadians, including Granatstein believe that the lessons from Dieppe were obvious and the mistakes made had little justification. I suspect the truth lies somewhere in the middle between that view and the fact that what seems obvious in retrospect is often far from obvious.
South Dakota, North Dakota, and North North Dakota
The Alamo wasn’t exactly pivotal in a military sense; it, along with Goliad were more significant with respect to just how serious the Mexicans were- they besieged the Alamo for 13 days, finally storming the fortress and killing the defenders to the last man. And at Coleto/Goliad, they defeated the Texans, and then massacred rougly 430 Texan captives.
Those two events started the “Runaway Scrape”, where the Texans generally fled eastward, and Sam Houston marshaled his forces and eventually caught the Mexican Army by surprise at San Jacinto. (see my post upthread about that battle for more information).