Since April 2008, legislation in the US requires NIH-funded authors to deposit their manuscripts in PubMed Central (PMC), unless they publish in one of the journals which are already depositing published articles in PMC (list here). Authors publishing in the Journal of Medical Internet Research (JMIR) are exempt from the deposit requirement, because - since inception - JMIR is already depositing all published articles in PubMed Central. JMIR is only one of 2 journals in the health informatics / ehealth field where NIH authors can publish without going through the deposit process. Other funding agencies that require funded principal investigators to deposit their author manuscripts in PMC (again, authors publishing in JMIR are exempt from this requirement as JMIR does it for them) include CIHR, Wellcome Trust and other UK foundations, Howard Hughes Medical Institute, and private foundations.
Principal Investigators not complying to these open access policies will face problems with obtaining future grants or may face other sanctions.
Another advantage of publishing in an open access journal from the outset (as opposed to self-depositing manuscripts) is that we deposit the copyedited, published version of the article, as opposed to the raw non-copyedited author-manuscript - authors avoid that people read and cite different versions of the manuscript.
Consolidated Appropriation Act, Dec 26, 2007: "The Director of the National Institutes of Health shall require that all investigators funded by the NIH submit or have submitted for them to the National Library of Medicine's PubMed Central an electronic version of their final, peer-reviewed manuscripts".
The Omnibus Appropiation Act of March 11, 2009 made the policy permanent (P.L. 111-8)