I think it really depends on what qualifies someone as a great military commander in your mind. When it comes to setting up and fighting battles and battle strategy in general I dont think theres any real way to deny Hannibal's brilliance he massacred every army Rome could throw at him (many times with far less men then Romans). When it comes to the general war strategy (Hannibal's strategy was entirely battle centric) I think its fair to cast doubts because he honestly never stood a chance at defeating Rome. He had no siege equipment to make attempt at capturing/buring Rome and simply by refusing to engage Hannibal in battle (preferring to harass his supply lines and forgers whittling his army down through attrition) Rome could not lose the war. In my mind he is a great battlefield tactician/commander but not the greatest of military strategists as his strategy for victory against Rome never really had a chance.

Hannibal's reputation stems primarily from the school of military history which subscribes to the idea that war is primarily a series of battles, and that the victor is the side that won the most battles. In this regard Hannibal was an extremely successful general who won many battles, most notably Cannae which was Rome's single greatest battlefield defeat in its entire history.

The problem is that war is not a series of battles and victories. It is ultimately a contest of nations, and nations are ultimately powered by their economy; and the economy in turn is directed by politics (which at its core is about the government's attempt to parcel out limited resources). Rome may have lost most of its battles against Hannibal, but its economy and political power was much stronger which allowed them to replace their losses even when Hannibal was campaigning in their Italian heartland. By contrast Carthage as a nation was defeated when Scipio Africanus landed an army in Africa and defeated Hannibal in just a single battle at Zama. They simply could not replace their losses the same way the Romans did.

That said, the "decisive battle" school tends to hold Hannibal's strategy - which was to march across the Alps and bring the war to the Italian heartland - in high regard; as they believe the only way Carthage could have won was for Hannibal to bring his superior tactical skills to play and inflict a series of crushing defeats on the Romans until their power base was destroyed. And as noted by other posts, there is a debate whether this meant actually capturing Rome or breaking Rome's hold over other Italian cities.

I instead offer an entirely different view point: I believe Hannibal's invasion of Italy was a grave strategic miscalculation from the outset.

It bears remembering that the purpose of war is not necessarily the complete destruction of the opposing state. "Total war" - involving the complete destruction of the enemy state - is a rarity and not the norm. By invading Italy and threatening the Roman heartland Hannibal in fact drew Carthage into a total war situation, which was disastrous given the strategic disadvantages of Carthage. Hence, rather than being a brilliant "solution" that gave Carthage its best chance of winning, Hannibal's strategy in fact basically destroyed any chance of Carthage remaining a major power by forcing it to fight an all-out battle against a superior opponent. Indeed by some accounts this was Hannibal's entire point - these accounts claiming he absolutely hated the Romans and wanted them destroyed as part of a long family grudge - except it never occurred to him that Carthage may end up destroyed because of his actions.

Moreover, the march over the Alps was a tactical disaster in its own right. The Romans may have lost tens of thousands of soldiers in battle at Cannae, but Hannibal lost his own tens of thousands in the winter in the Alps. From a "battles" stand point Hannibal may have the higher "score", but from an overall casualty standpoint his losses to the winter in the Alps pretty much erased any material lead he may have had.

A stronger strategy for Hannibal would have been to remain on the defensive in Spain and Africa. He would not have lost so many men in the Alps, and his tactical skill would allow him to beat the Roman armies sent against him, especially since he would be fighting on friendly ground. This would hopefully erode Roman support for the war - particularly since they could not muster popular support against an existential threat in their heartland - until an equitable peace could be reached with the Romans.

In the end of such an alternate scenario Carthage would not have destroyed Rome, but it would have survived and would not have simply been erased from history as was the case in the Third Punic Wars; at which point it was already powerless militarily.

Hence, Hannibal is a dangerous example. His strategy revolved around giving the military the best chance of winning battles, without considering the wider political and economic issues that would determine who would win the war. Indeed, it can be argued that Germany in the First World War - whose initial war plan was inspired in large part by Hannibal and Cannae - fell victim to this trap of creating a strategy that maximized the chance of winning battles without considering if these battles should have been fought in the first place.

Edit: Clarifications.

In my mind, Hannibal was unquestionably one of the greatest military commanders of all time, comparing favorably against both Alexander the Great and Pyrrhus of Epirus, who he ranked ahead of himself.

Hannibal successfully led his army from Iberia into Italy, at a time that such a thing was considered impossible such that he audaciously appeared in the midst of the enemy when they least expected it, and subsequently defeated the two major Roman armies in the field.

From there, he sustained a campaign in the heartland of his enemies' territory for fifteen years virtually cut off from any assistance by the motherland. In doing this, he presided over a multi-ethnic army that must surely have spoken a dozen languages, made up of different people that each had their own agendas and prejudices towards not only Rome but also other components of his army.

Ranged against him was the might of the Roman war machine, with its highly motivated and qualitatively excellent soldiers, able to continually replenish losses without ever a thought towards peace. It was Hannibal's misfortune to be fighting the Romans, when any other people in the world would have surely sued for peace a dozen times over.

And even so, the Roman's ultimate answer for Hannibal was simply to avoid fighting him. That the most relentless country in the world would have adopted this attitude at all, towards Hannibal alone (never against Pyrrhus, or the Cimbri) is perhaps the most fitting tribute you could bestow upon Hannibal Barca.

Against Hannibal, I'd only place Caesar himself as a greater commander because the latter sustained similar circumstances - a campaign lasting years and years amidst a hostile country with little support from the motherland. Even though Caesar was ultimately successful, you can't help but observe that he at least had the advantage of fighting with a highly homogenous, effective army against opposition that was oftentimes militarily ineffective. For Hannibal, the circumstances were often exactly reversed.

I would say that of all the generals of antiquity, Hannibal consistently did the most with the least, sustained battle the longest, and won the most undying enmity - and respect - of his greatest adversary.