Open Access Success Stories?
The great success story of open access is arxiv.org.  Wikipedia claims that "in many fields of mathematics and physics, almost all scientific papers are self-archived on the arXiv repository."  There is no citation for this claim and I couldn't find a study, but certainly there are subfields where a very high fraction of papers go on arXiv.org.  

It's also a fact that all serious journals in these fields allow authors to post preprints on arXiv.  I would say that "all authors can make all their papers freely available with minimal effort" is success.  This latter statement is backed up by data; just go to SHERPA/RoMEO and search for e.g. journals with "math" in the name.  The first page of 50 results doesn't show a single one that prohibits preprint archiving.  

The dominant publisher (SIAM) in my field (applied math) allows authors to post the final published article on personal or institutional websites, for no charge.  When they adopted this policy, they also made it apply retroactively to all articles ever published by them.  I'd call that success.

I wouldn't necessarily consider a wholesale move to author-pay journals to be a similar success, since the author-pay model (as implemented by many for-profit publishers) siphons off just as much money that was intended for research as the (for-profit) subscription model does.