Does gravity travel at the speed of light? Whenever I did calculations in high school physics involving gravity, it was either "a ball falling to the earth" type scenario, or a basic measurement of the gravitational attraction between two planetoids. 
I think I read somewhere recently that gravitational changes "aren't reflected instantly across the universe but instead propagate at the speed of light" somewhat like the ripples in a pond expanding. 
Is this true? Is there experimental evidence to confirm or deny this? What is the theoretical basis for it?
 A: 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.
A: To simplify Dan Neely's answer, gravity propagates in Newtonian theory (high school physics) instantaneously. Gravity propagates in Einsteinian theory (General Relativity) at precisely the speed of light. In the real universe, it looks like probably the speed of light. Lots and lots and lots of evidence indirectly indicates that it is so but no one has yet succeeded in directly measuring gravity waves.
