HereHere is a proof-of-concept video, illustrating a system using TNT. The cobble is generated and blown up by TNT; and then transported by water to (presumably) a hopper. There are other ways to achieve the desired effect -such as using creepers/withers/etc (through a monster spawner or darkened room) - which could be done, for example, by using creepers and ocelots with directing corridors, to get the creeper to where you wanted him to go.
If you're looking for an easy way, just get a whole bunch of gunpowder and make loads of TNT. Otherwise, I'd suggest trying the "creeper and ocelot" method.