I agree that the standards between US and Europe seem to be different, the US seems to be much more opposed to this than European institutions.
When I was applying to grad programs I was told that it's considered a form of academic inbreeding to go to the same university where you did your BS and get a Ph.D. I even spoke with a faculty member at my alma mater and he told me that they don't even look at applications from people who have done their undergrad there. It has to do with what Yggdrasil is saying; you're supposed to be trying to expand your knowledge and view of your field. If you stay at the same institution for too long you become very indoctrinated by one line of thought and don't learn to see things in different ways. However, as Biopolmonkey said, if you're at a top tier university or the specific program you're in is very well respected then I think there's more likelihood that people will understand why you wanted to stay.
That being said, the institution where I did my grad work universally encouraged undergrads to apply for the grad program there and no less than 25% of all incoming graduate classes were comprised of undergrads that had gotten their degree there and had planned on staying with the same prof that they did undergrad research with. None of these people seemed to have any problem getting jobs or postdocs.
So the bottom line is that I was told one thing and did it, but then watched the opposite thing happen and work out for lots of people. To be honest, the availability of jobs and postdocs seemed to be more influenced by economic conditions than anything. Lots of grad students from my program locked up good industrial positions without postdocs a few years ago. This year everybody took a postdoc, there isn't a single person I can think of that got an industrial position. I will say that moving around and seeing different places and institutions is very cool, I have enjoyed it a lot and encourage everybody to do so (although I understand not everybody is in a situation where they can manage this easily).