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Wondered this for a while, and I suppose also whether magnetism and other forces have a speed.The speed of light applies to anything with mass, i think! But does a graviton have mass, if not why cant we find them?...thanks! 
Van Flandern made some important discoveries that were rejected for many years - but his denial of GR and other off the wall theories (faces on mars etc) are so beyond mainstream to be slightly crackpot.
Imatfaal"and do you have a link to the SciAm article - I would love to read it"I cannot find a reference to the SCIENTIFIC AMERICAN article but I think it was a somewhat simplified version of this paper for lay readershttp://arxiv.org/PS_cache/gr-qc/pdf/0601/0601043v1.pdf
Syhprum - I am not sure that heresy is the best way of describing it, but I know what you mean. I disagree with you, but I know what you mean; the immense pressure to conform to scientific mainstreamism is damaging, it creates doubt through its own need to say everything else must be wrong. The better method of defence is "GR works, bring me something else that works and I will try that too" there is no other consistent theory that will let you put a satellite into orbit around mercury, get the gps atomic clocks working properly, and correctly predict the amount of gravitational lensing etc. As soon as the non-classical theories were shown to have great predictive power it became clear that GR cannot be the whole story because of the contradictions between the two - but in the classical limit GR works blindingly well.
There's currently searches for gravitational waves (for ex. LIGO: http://www.ligo.caltech.edu/). If these waves are found and agree with general relativity's predictions, then we can be pretty confident that gravity moves at the speed of light.