NSF's Grant Proposal Guide section I.E addresses eligibility. [I.E.3](http://www.nsf.gov/pubs/policydocs/pappguide/nsf15001/gpg_1.jsp#categories) addresses for-profit corporations and states:

> 3. For-profit organizations - US commercial organizations, especially small businesses with strong capabilities in scientific or engineering research or education. An unsolicited proposal from a commercial organization may be funded when the project is of special concern from a national point of view, special resources are available for the work, or the proposed project is especially meritorious. NSF is interested in supporting projects that couple industrial research resources and perspectives with those of universities; therefore, it especially welcomes proposals for cooperative projects involving both universities and the private commercial sector.

My read of this is that it is certainly possible for a company to submit a proposal, but the introductory language certainly hints that not all programs will allow for-profits to submit: 

> Except where a program solicitation establishes more restrictive eligibility criteria, individuals and organizations in the following categories may submit proposals: 

Which is to say that many RFPs limit submissions to categories 1 and 2 from that list (universities and other non-profits, respectively).