Rail transit projects typically cost about 40 to 50 percent more than projected, with some projects costing double the original projections and very few costing less than 20 percent more than the projections. The table below shows the projected and actual costs of 56 rail projects (and four bus projects). Most of the data are from a series of Department of Transportation reports, the first of which came out in 1990 (23.5 MB), with updates in 2003 (17.2 MB), 2007 (3.7 MB), 2008 (0.3 MB), 2011 (0.7 MB), 2012 (0.1 MB), and 2013 (0.8 MB).
I added five projects to those listed in these reports. One, the Los Angeles Blue Line, is documented in a 2006 paper by researchers at Northeastern University. All of the numbers in the paper are identical to the numbers in the 2007 DOT report except that the paper also has the Blue Line while the DOT report does not. I presume the methodologies are identical and that the 52 rail projects in the DOT reports and the Northeastern University paper are a representative sample, as the FTA would be unlikely to deliberately bias the sample to projects that went over cost by more than the average.
The other four projects I added were completed since 2009, the date of the last project studied in the DOT papers. I based the data for these projects on FTA New Starts reports and other official documentation. My selection of projects may not be as representative a cross-section of projects completed in that time period as I only picked projects I know about and these may tend to go over cost by more than the average.