I've been very interested in this subject for quite some time and have done some number crunching on employment rates in different sectors (as determined by our national statistics agency). Practically of them are in decline except for these five:
- Medical and other care
- Sport and recreation
(and to a certain extent waste management/recycling)
Jobs in these sectors have been growing steadily for the past 40 years. I think we can expect that trend to continue; these are exactly the jobs that are not easily automated. The others will slowly be taken over by the machines. This in itself is not a problem, though. The problem lies not in automation, humans will find new things to do. There is a problem though, and that's that as humans are replaced by machines, the money earned by these machines will be "trapped" within businesses. Without employees, there's no salary to pay and there will be no mechanism to keep the money going around. Economy will slow down, possibly come to a standstill. And this may very well be exactly what we've been experiencing the past few years (albeit partly caused by outsourcing to China instead of automation - for now).
There are several "solutions". The obvious one would be huge taxes and welfare. However, as stuff becomes automated really quickly, nearly everything businesses currently do will become commodity rather quickly. On the one hand this means everybody can do them, on the other hand it means nobody will be able to excel in them nor will any new business be able to enter such markets. Due to this, probably not too many businesses will remain. And when that happens, we will end up in some kind of planned economy. If we smart and/or lucky, that is; the alternative would probably be some kind of dystopian oligarchy of the owners of the machines.
Marshall Brain wrote quite a nice story about exactly this situation, its problems and the possible solutions. For a story it's rather bad, but it provides so many insights into the intricacies of this problem that it's definitely worth a read.