See sci.physics FAQ part 2,
<URL:ftp://rtfm.mit.edu/pub/usenet-by-hierarchy/sci/answers/physics-faq>, 
(for North American sites)
<URL:http://math.ucr.edu/home/baez/physics/faq.html>,
<URL:http://www.public.iastate.edu/~physics/sci.physics/faq/faq.html>,
<URL:http://www-hpcc.astro.washington.edu/mirrors/physicsfaq/faq.html>,
(European sites)
<URL:http://www.desy.de/user/projects/Physics/faq.html>, and
(Australia)
<URL:http://www.phys.unsw.edu.au/physoc/physics_faq/faq.html>.

Short answer: yes in GR, not necessarily in other theories of gravity;
experimental limits require speed very close to c.