e.g. Dan Shechtman, who recently got a nobel for his work in crystallography, was an outcast for a long while because his data did not fit with the prevailing model - to the point that people in his lab refused to peek through his microscope eyeviewer because what he said they will see there should not have been possible.
Read http://www.theguardian.com/science/2013/jan/06/dan-shechtman... and also http://motherboard.vice.com/read/quasicrystals-are-natures-i... (it's about a lot more, but also talks about Shechtman's history)
There are a few other cases like this: Robin Warren (Ulcer/Helicobacter connection), Barbara McClintock ("Jumping Genes"). The farther back they are, the harder it is to get the real story, but unfortunately Shechtman's story is far from unique.