Where will it end?

We've only just begun to work with bio-tech chips. There's no end in sight.

working with todays chips which are growing in speed, they will at one point reach a stalemate. You must remmeber that the chip is only as fast as the board lets it go. Todays boards suck and as a result, the chips we use are not fully pressed. They could go faster if the new technology would be released.

Like Brian said there is bio-computing. Then there is the truly stange quantum computing, not only would chips be even smaller but here could be multiple 'states' (not just 1 and 0).
When the multi-processor people get things cranking not only willcomputers use processors orders of magnitutde faster but there will be dozens (hundreds, thousands ??) of them linked to speed processing even further.