The Center for Housing Policy recently released a brief that reviews the research on this topic. The general finding is that in many cases, it does. The average impact is relatively modest but can be quite large depending on a variety of factors.
Characteristics that appear to lead to housing cost increases include: new rail service that dramatically increases regional accessibility; fast and frequent service; and station area development that is walkable and mixed-use (rather than auto-oriented). Higher housing costs and development activity are also more likely to occur in strong real estate markets and in cities that incentivize such development.
The research also identifies a handful of studies that find neutral or negative impacts due to the "nuisance effects" that can be associated with fixed rail transit.
Because of the variation in the types of public transit systems, their regional contexts, the research methodologies, and the data available, it is impossible to predict the precise impact of new or expanded public transit in a metro area that is considering such an investment. There are too many moving parts. But the research suggests that, more often than not, housing costs will increase, and they will do so early in the system's development stages.
If anyone has first-hand experience of how public transit has impacted housing costs in their area, I'd be very interested to know whether they were in-line with these conclusions.