The transition to a self replicating, all-purpose widget machine, will be rough, extremely so. But humans will adapt. Ants go about their day regardless of the might&majesty of human beings.
As foolish as it may be to make predictions (and leaving aside whatever new problems/possibilities arise; ) if we're gonna leap with both feet may as well speculate that:
-The relation between man and 'bot will be as symbiotic as that of man and dogs. At least at first. Robots will need to learn how to pick up on our social cues if they are going to get far on this planet.
-The super fantasy ultra intelligent robot that overcomes and goes beyond the limitations of its human creators may very well not be all that much interested in us meat bags. There's a chance it rockets itself into space/shuts itself down/"blows everything up" as much as there is a chance that it is a malevolent or benevolent force in our lives. We may build the thing only to find ourselves abandoned and stuck with ourselves.
-I expect a lot of artisanal, avocational and hobby-like activity will be the order of the day. Entertainment/distractions will not be going anywhere. There will be a great push by some to make everything the product of Mr.Roboto but people will ignore it by a certain point. The thing people-who-await-the-robot-singularity forget is that for most, their fascinations begins and ends with other people. They may find satisfaction, companionship and amusement with humanoid robots but it will always depend on the humanoid part. Enough people will be wowed by the local guy who makes poorly made chairs and will rationalize why they want that guy to make all their furniture. A future where all needs can be met efficiently by non-humans and non-humanoids will quickly show how most people are satisficers and will be uninterested with maximization.
-Robots may very well find it convenient to task and store large chunks of information with human beings, at least as backup. For all the griping about our memories or learning capacities, communities of us are nifty information storage units just roaming out there. It is true it sometimes takes decades to train us in certain fields but a Mr.Roboto may very well be thinking in centuries and millenia...a 20 year training for a fifty year+ self-replicating, adaptable memory unit which can survive and adapt to emergency conditions may be a good back up option compared to having to rebuild units of itself over and over and over again while using up energy and materials.
-The basic economic unit is the gift. And gifts between men deal with future value in the face of desires, designs, imitation, uncertainties all mediated through demand and scarcity. The economic progress of humanity up until now has been to figure out how to extend "gift-giving" capabilities within larger and larger networks. With super-robots doing all the hard mental and physical labor, who knows how this plays out? The current system has its good and bad points, and that's well-trodden now....but how do we not slip into hard statuses and avoid extreme decentralization when the means of production and its labor is controlled and watched over by machines of loving grace? Not to mention that skullduggery that will happen when the real transition begins and the remaining human capital pools into the hands of a few (like in the transition during the industrial revolution). Unlike the rise of industry, having robots capable of anything will give those owners the capability to do anything. Wipe out humanity, establish themselves as kings and queens, determine how the robots behave forevermore....the potential capriciousness and tyranny is more frightful than the loss of work as we know it. If we survive that alright, we come out the other side with the ability to unite the whole planet as one or shut ourselves off in little cliques and communities. All sorts of weirdo arrangements could be and probably will be tried.
-The economy will likely be run in some sense on sustainability. Maybe people will earn credit not so much by satisfying a demand as filling a niche. So if you want to sweep streets, run a small farm, count sheep; great! It will become a question of remaining active, role playing and making sure your business is not too materially intensive or wasteful. I can see whole industries arising where the job is just to be a living witness to some specific role in a historical period. Some guy will be tasked with being the bartender in a wild west saloon; a serf in 8th century France, a hunter-gatherer post-Ice Age...the accuracy may not be there, but the robots may want to study humans in "old human habitats" and it leads to these virtual jobs for social anthropological purposes. It's a future of servants and bureaucrats- how does that go?
-There will be an appreciable number of people, and great pressure, to worship the robots as gods or make idols of them. A whole bunch more will be lost to the virtual. There will be a certain cruelty done to those who won't, or can't, conform. The virtual will be a prison for a number of these people. As easy and benevolent as these super systems can be, it will take one bad seed with malicious intent to do real damage with the robots.
- "Shove 'em full of drugs" is a creepy response to a creeping robot future. I don't trust the robot future because I find much of the push for a robot future to come from people who seem rather misanthropic. I do not know if it is a prejudice on my part or if that is the prejudice of the people determined to reach a post-human stasis.
-Maybe Star Wars, for all its awfulness, has it right. The future of work will be primitive playpens with no purpose or consequences. Because underneath the farm habitat, the local, bartering bizarre, the seedy tavern will be this very complicated robot economy that takes care of all your health, security and ecological needs. Lose a hand? Just get the robots to fix it. Need interstellar ships? No one knows how to build them but the robots...everyone runs around playing cops and robbers with little awareness of science or technology or humanities. But they make it work and go on living.