We have a number of roundabouts in extremely high density traffic areas in my own hometown (located in the USA I might mention, though some are of the opinion that California's national status is debatable) and they manage to provide for a means of high speed/stakes/terror transit that results in almost no actual mishaps and a great deal of expediency.
roundabouts have been recently (5 years) installed in my city here in Canada. Overall, the concept is fine. but the major current problem is the idiots driving in it and sometimes the size of the roundabout.
If its diameter is too small and you have two lanes, it will not give enough time to drivers to enter it without having to crush the gas pedal... and if you have too many lanes... You may end up with this:
Best is one lane, or two if the diameter is big enough.
In Croatia Roundabout are quite often, you can find them on bigger crossroads, where traffic lights would be just to complicated to build, I find it very simple and effective way of solving traffic jams. And I haven't seen many accidents happening around them. It works quite simple, people who are driving in it have advantage over those who want to enter it. So you just wait till it's empty or there is hole where you can hop in.