It's no easy task to accurately weigh the pure effectiveness of a military force. How much of its skill derives from its leader? How much of the society's technology benefited it? How much is just historical luck? These things are, of course, inseparable, but this is all about the military forces that would win in an all-out brawl, not about generals, technology, or circumstance.
In considering this, there a few unfortunate but necessary exclusions. Any modern army would completely devastate ancient forces. Not just because high-yield explosives and rapid-fire guns would easily overpower sword and shield, but because modern tactical planning, surveillance, and reconnaissance are so advanced that comparison becomes nonsensical. For this reason, the list will be limited to pre-rapid fire armed forces. Some early gunpowder troops will be included because the long reload time would allow hand-to-hand troops the opportunity to close the distance and engage.
Then there is the matter of terrain. The fierce desert forces of Shaka Zulu may have had a little trouble adjusting to the densely wooded combat of Northern Europe, and the fiercely mobile Mongol cavalry would have found combat in the rainforests of Central America challenging. It's a mark of skill for troops to be able to fight well in any terrain, from open plains to urban environments, but in this case, terrain should not be considered much.
These are some of the fiercest, most disciplined, and most effective fighting forces in human history. If they were to fight, however, there can only be one true victor.
Who and When: 509 BC-476 AD, centered in present-day Italy. At its height, the army was as much as 700,000 men strong across the Empire, but a single army would consist of 25,000.
How Much They Conquered: The Roman Empire's western border was the Atlantic Ocean on the Spanish coast. It spread to Britain in the north, North Africa in the south, and deep into the Middle East.
Their Arsenal: The Roman army used siege weapons, such as ballista, as well as cavalry and military engineers, but the backbone of the army was the heavy infantry. These were tight formations of soldiers who used long throwing spears (called pila), as well as a short thrusting sword in closer combat.
Their Training And Organization: Rome was an intensely warlike state, meaning it was possible for a man to make a career as a soldier. As a result, their troops became highly trained and disciplined over time. The armies were organized into legions, each of which had between 800 and 1,000 men.
On The Battlefield: The Roman legions were shockingly effective against opponents as varied as the Carthaginian army, the German tribes, and the Macedonian Empire. They accomplished this through the use of a tight defensive formation that was often three ranks deep, with light infantry up front and heavier infantry in the rear ranks. This tight, practiced formation allowed the senior soldiers to motivate the raw recruits (and guaranteed that the less-experienced soldiers would be the first to perish). Another important element of Roman tactics was the use of quickly built wooden fortifications, sometimes constructed overnight, which made the Roman position incredibly hard to break.
Weaknesses: Occasionally, the Roman Empire was a victim of inflexibility. If they faced a truly brilliant general, they could be trapped in their formations, unwilling or unable to adapt to their opponent, such as when the general Hannibal crushed a much larger Roman force at the Battle of Cannae.
Who and When: Genghis Khan began his conquests in 1209. His average field army was around 100,000 men.
How Much They Conquered: The Mongol Empire almost entirely dominated Asia. It included China, Turkey, much of the Middle East, parts of Russia and Eastern Europe. To this day, it is the largest contiguous land empire the world has ever seen.
Their Arsenal: The Mongols tended to be heavily armed with a combination of daggers, maces and sabers. However, their true technological innovation was their finely made composite bows, which could fire at double the range of comparable bows in Europe at the time.
Their Training And Organization: The European conception of the Mongols as a "horde" of undisciplined, ferocious monsters was completely inaccurate. True, they were terrifying in combat, but their tactics required extreme discipline, which was enforced through punishment and rewards, encouraging acts of bravery and discipline. At the same time, Genghis Khan was a brilliant administrator, and his skill with organizing supply lines for his massive, mobile troops was unparalleled.
On The Battlefield: The Mongols' incredible success is often boiled down to their mounted archers, and it's true that the incredible skill of these soldiers, combined with Khan's notorious false retreat tactic, led to many of the Mongols' victories. However, cavalry alone would not secure an empire of this size. The Mongols would also routinely hire Chinese artisans to construct siege weapons if they had to break a city. They also pioneered some of the most advanced techniques in spying and propaganda the world had ever seen. This would often cause cities to simply surrender, allowing the Mongols to then press the citizens into service.
Weaknesses: Like any other cavalry-based force, the Mongols had significant trouble in areas where there was not space to maneuver.
Who and When: Alexander reigned from 336 to 323 BC. When he crossed the Hellespont in 334 BC, his forces numbered roughly 20,000 men.
How Much They Conquered: Alexander started from Macedonia and headed east. By the time he passed, he had conquered a vast swath of territory that reached all the way to the Indus River.
Their Arsenal: One of the chief innovations of the Macedonian forces was the use of a sarissa, which was a phalanx spear longer than most spears of the era. This core of phalanx was supported by cavalry and some of the most advanced siege weaponry available, in the form of catapults and siege towers.
Their Training And Organization: Alexander owes much of his success to his father, Philip II, who took a disorganized and weak fighting force and turned them into a powerful machine. He did this by reorganizing the forces into phalanx, instituting strict punishments for disobedience, and constantly drilling the members of the core phalanx.
On The Battlefield: Alexander's tactics rarely varied. The Macedonian army would form up into phalanx eight ranks deep, and thanks to their extraordinarily long spears, as many as five layers of spears protruded past the first rank in this formation, turning the phalanx into an impenetrable wall. In less disciplined hands, this would turn into a chaotic scramble, easily broken by flanking or cavalry. However, the Macedonian troops were so well trained that they could break off into multiple divisions and form new fronts against flanking attacks.
Weaknesses: The success of the Macedonian army may have been inseparable from the genius of its commander. Would the Macedonians stand a chance without the tactical genius of Alexander leading them? It's impossible to say for sure, but after his passing, the Macedonian conquests ended, the empire fell apart into multiple successor states, and the military never again reached the same level of greatness.
Where and When: Sparta, Greece, 6th century to 4th century BC. Their numbers are largely unknown, but they frequently suffered from a shortage of Spartan warriors and supplemented their ranks with mercenaries and slaves (helots).
How Much They Conquered: After conquering Athens in the Peloponnesian War, Sparta essentially controlled the entire Greek world.
Their Arsenal: The Spartans, like many ancient forces, were equipped with long stabbing spears (doru), short stabbing swords (xiphos), and a large shield (hoplon).
Their Training And Organization: Sparta would only allow the fittest children to become warriors. They lived under constant supervision, and the elite male citizens were trained for nothing but battle from the day they were born. This included intensive physical training, as well as a thorough indoctrination in Spartan wartime philosophy and battle tactics.
On The Battlefield: The Spartans favored a phalanx formation. Indeed, the Spartans became so identified with this tactic that their elite warriors were called hoplites after the shields they carried. In combat, the Spartans interlocked their shields, leaving space for their spears to protrude. This turned them into an impenetrable wall, and any opponent that managed to get through the spears alive was quickly hacked to pieces by Spartan blades.
Weaknesses: The Spartans' main weakness was moral, rather than military. They treated the helots brutally, and because of their treatment there were many uprisings. These helots were responsible for Spartan supply lines, fortifications, and all manner of support. Clever propaganda could cause an uprising and cripple the Spartan forces.