What makes this question difficult to answer is the degree to which these larger trends and evolutions were actually intertwined with the key personalities of the Roman Republic. In these respect, individuals like the Gracchi Brothers and Gaius Marius were critical in shaping the later conditions that led to the civil war.
I would suggest one of the key factors in shaping the fall of the republic was the expansion of Roman power across the Mediterranean world, beginning with the wars against Carthage. This dramatic increase in territorial size brought with it vast amounts of wealth, furthering the inequality that had always been present within Roman society. At the same time, the growing size of Roman territory, and the need to defend that territory, brought with it new demands on military administration that would be critical in shaping the later disintegration of Rome's political order.
It was within this context of empire that we see some of the most important personalities in this drama begin to emerge. In a period already marked by growing inequality and social strain, the Gracchi Brothers channeled these resentments as populist politicians, utilizing widespread popular support as a weapon and a tool. In addition, you will find another key personality in Gaius Marius, the great military reformer, who shifted the Roman military from a levy based system to a professionalized army while lowering the property requirements that had previously been imposed. This had the effect of greatly expanding size of the army, but at the same time, more than ever before, Roman soldiers would become personally loyal first and foremost to their legates (as you can perhaps see in the history of the civil wars).
In this respect, it is actually very difficult to separate the great individuals from the larger social, economic and political trends that shaped the fall of the Roman Republic, given the degree to which they are actually intertwined. The dominant figures acted within the larger context of Roman expansion across the Mediterranean, but through their actions and examples, they actually contributed to (and in some cases, perhaps, even created) the instability that would plague the late republic.