Rules for rotary/roundabout? Does a cyclist have the right of way in a traffic circle/roundabout/rotary (in the US)? Any tips for riding around one of these scary things?

This past summer, I was riding around a rotary (a.k.a. roundabout) and a driver behind me wanted to leave the rotary, by turning right. Because she was driving faster than me, when she tried to turn right she almost ran into me and had to screech on her brakes - then proceeded to yell "You should have used your hand signals" to me, even though I wasn't turning (I was just following the rotary around). I am almost certain I was following the rules, am I mistaken?

I guess the rules go out the window sometimes anyway, and you have to watch your own back...
Yeah, in theory you should ride near the left edge of the right lane (if multi-lane) until you get near your exit point, at which time you mosey to the right -- "own your lane".  This is basically the same way you should ride on a road with shoulder when the shoulder converts to a turn lane.

In practice, I suspect I'd be tempted to stop, dismantle my bike, and mail it to the other side at many of the rotaries I've seen.

Keep in mind that folks in the US are largely unfamiliar with these beasts, and are often seriously confused by them.  They can easily miss seeing a bike in the confusion.