A new study in the Journal of Transport Geography suggests that four light-rail systems built around England during the 1990s and 2000s had virtually no effect on overall car traffic. Instead, the rail systems mainly seemed to attract riders who would otherwise have taken the bus.
Now, this is only one study. But as Jaffe notes here, other research on this topic has also been surprisingly inconclusive. One study did find that Denver's light-rail system, built in the 1990s, cleared up some congestion downtown. But other papers have found that there's so much demand for road space that light-rail systems often have minimal effect — every time someone gives up his car, another driver takes his place on the road.
There seem to be two broad takeaways from this research. First, cities have tried all sorts of ways to alleviate their traffic woes, from building new highways to expanding public transit. The only policy that ever seems to consistently work is congestion pricing — charging drivers for road access in busy areas and during peak hours. Congestion pricing that's combined with expanded transit options like light rail seems to have worked well in cities like Stockholm. But light rail on its own appears to be insufficient.
The other point is that mass-transit systems can lessen road traffic, but only if they're part of a broader shift by a city to move to denser development. Researchers have found that people living in more compact cities with better transit options do drive less overall. But that shift doesn't happen overnight. And not all light-rail systems are even built with this sort of development in mind. (Indeed, as Jaffe notes, that appears to be the case with at least one of the English light-rail systems studied above, which was simply built alongside a new major roadway.)
Further reading: How Sweden managed to cut traffic congestion