I would recommend you [this excellent article][1] published in *Science* in 2011 that I previously posted [here.][2] There is proposal of one new robust measure together with exhaustive and excellent comparison with other ones. Moreover, all measures are tested on robustness. Note that this new measure is also capable to identify more than one functional relation in data and also to identify nonfunctional relationships.


  [1]: http://www.uvm.edu/~cmplxsys/newsevents/pdfs/2012/reshef-correlation-science-2011.pdf
  [2]: http://stats.stackexchange.com/questions/6421/what-are-the-breakthroughs-in-statistics-of-the-past-15-years/38901#38901