In general relativity gravity propagates at c. The rate of orbital decay of binary pulsars is, among other factors, dependent on the speed of gravity. The in-spiral rate of one binary pulsar system has been measured and found to agree with the rate predicted by general relativity to within a 0.2% margin of error.
Gravitational waves haven't been directly measured yet though (2012), so there's no direct confirmation. With multiple detectors currently in operation if a signal is detected and able to be tied to a specific location in space the timing delays between when its received between the two primary LIGO detectors (Livingston, LA, USA and Hanford, WA, USA) and the VIRGO detector (PISA Italy) should allow for estimating a propagation speed.
Advanced LIGO, expected to begin collecting data in 2015 is expected to be able to detect a number of signals so hopefully the question will be settled in a few years. However, there might not be any published results for a while after it goes active. The search for pulsar spindown signals with LIGO data is done via the Einstien@Home distributed computing project; and in prior runs several years passed between when the first part of the data set was collected and when papers on it were finally published.