There are those 'out there' who refute anything to do with with SR & GR because they see the theory as being purely 'mind experiments' not founded in reality.
This experimental test demonstrates that SR's and GR's time dilation and gravitational time dilation predictions have been measured, and are in accordance with the predictions.
This would seemingly eliminate the view that SR and GR are man-made, 'maths-based' conjectured models. Unfortunately, this view is unlikely to ever be yielded by those who make the accusations against GR & SR, as they are led by 'other' principles other than empiricism.
Other more historical GR supporting observations would be the
precession of Mercury (in arc-seconds per century):
Observed: 5600.7 +/- 0.4 arc-sec/century
Predicted by Newton: 5557.6 +/- 0.2 arc-sec/century
Predicted by Einstein: 5600.6 +/- 0.2 arc-sec/century
Source:
http://books.google.com/books?id=fp9wrkMYHvMC&hl=en
I believe GPS satellite clock correction factors are provided by GR theory as well, (although I don't know much about how this works).
Are there any others ?
Cheers & Rgds