Some thoughts
Okay, so population growth is pretty much exponential when you don't have any limiting factors (things like space, food, etc.). Well, space is pretty darn big, and with futuristic hydroponics and biochemical synthesis, I have a hard time believing that there would be much to limit population growth. As long as resources exist to build new structures to house people, in space or on a planetoid, populations would probably skyrocket throughout known space. Overcrowding? Just set your robots to work at constructing a new orbital station, or send out a ship full of adventurous newlyweds to that recently surveyed planet.
Stations would probably exist more as orbital living modules than outposts. Mining operations would not have much lack of workforce (either biological or mechanical), and resources could be exploited at a very quick rate in very large quantities. Even new colonies would probably not have much difficulty getting started, since their locations would have been selected out of potentially thousands, and the resources available would quickly allow for growth. After all, a sufficiently advanced space-faring society should have plenty of experience on setting up these new colonies. Launch a ring of satellites to scan the surface, drop down modular living pods to ideal locations, set up automated mining and terraforming equipment, and a self-suficient colony is created. In a few decades or so, people can start living outside of the pods. A few decades later, the first orbital habitats might begin to appear, all the while more people are coming from the older worlds.
Probably as a result of political power concerns, there would be plenty of emphasis on reproduction as a means to advance your new colony. I imagine a lot of large families would exist on newly colonized worlds, not because life is particularly difficult or dangerous, but because more births mean greater power. You can go to your interplanetary congress and demand greater representation, you have more workers for producing and consuming goods for a healthy economy, and should it come to it, you have a larger population base to create a militia to defend your planet in times of strife.
Core (established) worlds would essentially exist to consume resources and export people. They probably would have few resources of their own, although serve well as trade and governmental hubs, or serve as bases of operation for resource acquisition within a system. They'd only produce enough food for a relatively stable population, to keep a steady flow of people headed off-world. Overall inner worlds would be boring, fairly crowded, and mostly exist as economic powerhouses. After all, if you've got 50 billion people on a world and several billion more in orbit, that's quite a lot of economic influence on the galaxy. The new colonies have every reason to want to become like the established worlds.
And so... population growth continues at a very fast rate, pretty much without end. Each new colony spurred on through several phases. Initially, raw resources would be the most important in an agrarian society, eventually replaced by tourism as the primary focus (resource gathering is still full-force, however). After that, as less unused land is left, a more industrial economy might take shape, as resources are mined off-world and processed on-world. Technological gadgetry, shipbuilding, and of course orbital construction would take up the later phase. Entertainment might become a secondary focus, as well as anything requiring more human thought and effort, like the pursuits of science and the most important issue; figuring out how to fit more people on one planet, or move them more efficiently to others.
Anybody agree? Disagree? Other thoughts? This is sorta my random ideas topic for the month, so let's get a good discussion going.