How often do funding agencies require funded authors to publish their work in open access venues?
SHERPA, which produces RoMEO, also produces a database on funders' open access policies, called SHERPA/JULIET. There is a statistics page on the JULIET website. 

According to this page, 26% of funders worldwide require publication in an open access venue, 30% encourage this, and 41% have no policy.

When it comes to archiving the publication in an open access repository, 68% of funders require this, 12% encourage, and 17% have no policy.