First, who sponsors grant programs? There are basically two entities that award grants: Foundations and the Government. Within each of these, there are subcategories.
Foundations:
Private Foundations - these are normally organizations that are founded with money from an estate. Private foundations have the ability to fund various types of proposals.
Corporate Foundations - these are foundations set up within a company. Most of these grants are geared toward educational institutions and community groups.
Community Foundations - are foundations set up within cities, and almost always require the grant award to be spent within the community.
Operating Foundations
Government:
Federal Grants
Federal Block Grants
Finding the Perfect Grant
There are two schools of thought on finding a grant to write. The first school starts with the premise that you should know what type of grant you want to write, then research grant listings to find one that matches. The second school of thought is based on researching grants that are available, then writing one to fit. I am personally part of the latter - I think you should look to see what requests for proposals (RFP) are available, then write a grant to fit the guidelines. Regardless, there are many web resources for finding available grants.
http://web.fie.com/cws/sra/resource.htm This page, from the Society of Research Administrators, is one of the most comprehensive on the Web. It has links to all major foundation and governmental grants offices.
http://www.nsf.gov/home/grants.htm From the National Science Foundation, this has the most opportunities for math/science grant funding.
http://www.gsa.gov/fdac Governmental Grants can be obtained from the Catalogue of Federal Domestic Assistance.
http://www.fdncenter.org Foundation and Corporate Funders can be located through the Foundation Center
Develop Your Idea
The most important part of a grant proposal is the idea behind it. Without a winning idea, your grant has no chance of being funded. What makes a winning idea? There are five characteristics of a successful grant proposal: need, originality, creativity/problem-solving, reach, and timeliness.