John B. Anderson, a Republican, ran as an independent in 1980 and won 6.6.% of the vote. Reminds me of today's Trump insurgency, but Reagan is nowhere as abrasive as Trump.
One thing to understand about Anderson's bid in 1980 was that the Political Parties were much more diverse then. Their were still southern democrats and northern republicans. Anderson was running as a fiscal conservative social liberal. He drew much more of his support from disaffected democrats than republicans. White's The Making of the President is a classic source on this campaign. http://www.amazon.com/America-Search-Itself-President-1956-1980/dp/0446370983