Like any tool, roundabouts have to be used in appropriate situations. I used to work in traffic engineering, and adding roundabouts (or signals and stop sings, for that matter) requires careful study and the meeting of certain criteria (called warrants). Warrants include such things as daily vehicle volume, peak hourly volumes, pedistrian volumes, and delay times. In the right place, roundabouts allow traffic to flow better than a signal and with greater safety. Head-on and t-bone collisions (the two most dangerous types of traffic accidents) are virtually eliminated. The accidents that do happen will be at a lower speed and a gentler angle.
All of that said, there is always the problem of the unwritten "political" warrant. The mayor wants a stop sign (or signal or roundabout) here, so one is going in even if it is worse for the traffic. Of course, there are also fads to put in roundabouts (or what have you). Some of the roundabouts are going to be unwarranted or conditions will change. Roundabouts work best when applied correctly.