Number Five: Philip II
Philip was King of Macedon but has been understandably overshadowed by his son (more on him later). However, Philip himself was tremendously skilful, swift-witted and intelligent. When he came to the throne Macedon was in a weak position, and when he left it the kingdom had the strongest soldiers and most brilliant cavalry in the world.
He subdued the neighbours of Macedon and obtained hegemony over the Greeks. Had he not died it is entirely possible he would have had success as great as or at least comparable to his son.
Number Four: Scipio Africanus
Scipio became a general for Rome at a perilous time. A certain Carthaginian had slaughtered a significant percentage of Rome's citizens in battle, and in Iberia his father and uncle had been killed by other Carthaginian forces. Rome's best result so far in the Second Punic War was basically a draw against Hannibal.
Scipio was sent to retrieve the situation in Iberia, and did so masterfully. Through sound military strategy and diplomatic good sense he managed to destroy the Carthaginians in Iberia (admittedly Hasdrubal Barca was able to copy his brother's Alpine route from the peninsula). After this he went to Sicily and trained his army for a prolonged period, before being sent to fight Hannibal at Zama. Scipio had the advantage of more experienced soldiers but Hannibal remained a daunting foe for any Roman, having never before been defeated, and had more troops (although not very experienced ones).
Scipio won the battle, and with it ended the Second Punic War in Rome's favour.
Number Three: Aurelian
Not the best-known emperor, but he should be. Aurelian succeeded (after a brief contest) the Gothic Claudius as emperor in the 3rd century. This was a dark time for Rome. Her troops, once notable for their pathological patriotism, were now addicted to regicide and donatives (essentially a bonus given to soldiers when a new emperor arose, prompting many armies to force unwilling generals to declare themselves emperor) and the empire was in crisis. The Palmyrene Empire in the east had broken away, and the Gallic Empire in the west had done likewise. Furthermore, barbarians were invading what remained of the empire on a regular basis.
Fortunately for Rome it was led by probably the most militarily talented emperor in its history. Aurelian slaughtered not just one barbarian army, but many of them. He conquered the Palmyrene and Gallic Empires and returned Syria, Gaul and Iberia to the imperial fold. Without him the Roman Empire could easily have collapsed centuries earlier than it did. The Dark Ages would've lasted centuries longer and without the Byzantine Empire (founded by Constantine a century or so later) the Turks could well have overrun much or all of Europe.
Sadly he reigned for only five years, having been (rather predictably) assassinated. Had he been on the throne for longer he could have strengthened Rome even more.
Number Two: Hannibal
Hannibal Barca was blessed with tremendous skill and cursed with terrible luck. He set out to defeat Rome and enjoyed numerous successes, but ultimately failed. The Romans were staggered to learn he had crossed the Alps, in winter, in the teeth of barbarian opposition and were rather caught on the hop.
Shortly thereafter he defeated Scipio Africanus' father (whose life was allegedly saved by his son) at the Battle of Ticinus and defeated a second Roman force at the Battle of Trebia.
He also succeeded in arguably the most devastating ambush in Roman history (the Teutoberg Forest is the other contender) when he angered Flaminius into pursuing him and then launched a perfectly timed assault at Lake Trasimene. He followed this up by managing to slaughter a Roman army twice the size of his with the perfect tactics at the Battle of Cannae, showing tactical brilliance that is still revered today.
However, he was hamstrung by the stalwart loyalty of much of Italy (some, but not enough, deserted Rome), the political weakness of Carthage and the almost unbelievable patriotism and confidence that Rome possessed at this period of history. He could not maintain the string of stellar successes as the Cunctator held him off and a new crop of more skilled generals such as Marcellus, Nero and Africanus took command.
Number One: Alexander
Alexander the Great is one of the few men who really deserve the title. He did benefit from a wonderful inheritance, namely the finest army in the world, as well as a fine practical education in the military (he destroyed the elite Theban Sacred Band when he was 17) but he did even more with it than anyone could have predicted.
After slapping Greece about when it tried to throw off Macedonian hegemony he invaded Persia. There was not a city that did not yield to his will, nor was there an army that could withstand his own forces. Fortune smiled upon him too. At the Granicus Black Cleitus saved his life (Alexander would later do quite the reverse when he drunkenly killed Cleitus with a spear) and he survived being shot in the lung a short time before his death.
Persia was like a snake, and Alexander realised that defeating the head (the Great King Darius) at the Battles of Issus and Arbela would force the rest of the colossal Persian armies to flee. In India he faced more competent opponents such as King Porus, but prevailed there as well. The only adversary to best him was his own army which, after more than a decade away from their homes and families, refused to march any further east.
He died very young, in his early 30s, and his unborn son was a pawn that was eventually killed by the Diadochi who tore his fledgling empire apart as they struggled for supremacy.