As a Traffic Engineer I work with this issue frequently. Their are numerous benefits of roundabouts that outweigh the risks, so much so that numerous states, including New York, require the analysis of a roundabout at any new intersection.
The first issue is safety, roundabouts reduce what we call, Conflict Points, between pedestrians, bicycles and vehicles. The middle island also provides pedestrian refuge for a two stage crossing. Roundabouts also force cars to slower speeds which improves safety and reduces the risk of an automobile collision.
As far as delay and driver in vehicle perception, roundabouts statistically have a lower average delay than all-way-stop-controlled (AWSC) intersections for streets that have a volume of less than 20,000 vehicles per day. The Level of Service (LOS), is a measure of driver perception of service at an intersection. The average LOS for an AWSC at peak hours is F (Delay of 172 s), while a roundabout provides LOS C (Delay of 21 s). Both LOS determinations are for the best approach. So as you can see, the benefits are clear.
The downside is that many people are unfamiliar with them, a learning curve and the unwillingness to try out something new, as the adage goes, "If it ain't broke, don't fix it". Here is an example, I met with a consulting firm that performed a study in Buffalo, NY to put in a roundabout. The measurements worked and LOS would have increased for the approaches. However after installation the city council decided to put stop-signs at the roundabout approaches, against the recomendation of the traffic engineers. This was a foolish move on the part of the City as a major benefit to roundabouts is the Yield approach. Their is still no change to date.
It is an uphill battle but once people become more familiar you will see them throughout the US.
If you would like more information on roundabouts their are two resources from the federal government:
1. Roundabouts: An Informational Guide
2. NCHRP (National Cooperative Highway Research Program) Report572
Function reject.