There's a few here in Iowa City. People don't have a clue how to handle them. The one at the top of Grand Avenue has yield signs at every entrance (which, to me seems like common sense to yield to cars that are already there rather than ramming into them...). Enough people to make it annoying either barrel in without looking at all, or instead of *yielding* to traffic, come to a dead stop when there's no reason to.
The other really is just a circular island in the middle of a 4-way intersection. I tried to use it as a true roundabout once (going around a full circle) and almost got hit from several sides (well, not a REAL close call..). Since most of the traffic goes either 1/4 or 1/2 way around (right turn or straight through, if the island wasn't there) the other cars didn't even look to see if a car was coming or not, and furthermore instead of pulling in front of me (which would have been fine), waited long enough so they almost hit my passenger door.
There's a third one in north Coralville. It has two lanes going in, but there's a road sign marking the outside lane being dedicated for the first couple streets, and the inside one continues all the way around for the rest. That one actually works well (FAR faster to get through the intersection than the stop light that I'm sure they'd put otherwise), with one exception -- it's just outside the area the city maintains, so last time I used it a few years back, I'm going down a straight, dry road, get to the circle and it's 100% coated in ice. I didn't have any problems but the car did get a bit loose. There were loads of tire tracks off into the ditches, up onto the center island, etc., so obviously others had had more serious problems there.
I also saw one in Liberal, KS. That one was actually a proper full-sized roundabout.
But, in general, there's not a whole lot of them here. I've read theoretical talk about some towns planning to reduce the number of road signs, on the theory that it'll force people to actually pay attention while they drive instead of just following the signs and zoning out the rest of the time (and read that this does in fact reduce accident rates). Roundabouts would go in this direction I think. But in actuality, I've only seen an increase in signage.
Right on red? Generally it's fine unless there's a sign that says "no right turn on red" (as Tester says you must stop first though). I just wikipedia'd it, and they say the one exception is New York City, where right turns are prohibited unless the sign says they are allowed. As others say, you do have to come to a complete stop, and the guys with a green light of course have right of way.