If you're looking to raise funds for a project, activity or program of yours or an organization you're involved with, you're in luck. Many grants from many different kinds of organizations are available, in large part thanks to the American tradition of philanthropy.
Foundations and Individuals
Wealthy individuals sometimes have much more money than they can, or want, to spend in a lifetime. Rather than bequeathing all of their money to their family, many wealthy individuals choose to set up a foundation that gives away money to support causes the individual would like to support. Examples of foundations set up by wealthy individuals include the Rockefeller Foundation, the Soros Foundation, the Turner Foundation, the Kellogg Foundation, the Gates Foundation and the Carnegie Foundation.
However, sometimes wealthy individuals don't have a high-profile organization, but are still quite capable of giving a "gift" of thousands or millions of dollars to support work they feel is important to society or the planet. For this reason many charities and universities have salaried development officers who are charged with "cultivating" gifts or major gifts. Individuals who have a long history with your cause or organization, who personally know your founder or your board members, and who have previously supported similar activities or organizations with a major gift in the past are the most likely to give. Alumni of your school will also often be interested in helping other alums succeed.
State and federal governments typically have large sums of money they are responsible for distributing, though if you're dealing with a corrupt government the money might not all reach the designated target. Look for the branch of government that deals with the activity you'd like to fund; for example, if you'd like to set up an environmental education program, look for grants from the U.S. Environmental Protection Agency awarded for environmental programs in your state. If you're a researcher looking for funding, look for grants from the National Institutes of Health. The government also gives away money through its bilateral aid branches; as such, the United States Agency for International Development (USAID) -- the United States' official development aid agency -- awards grants for activities that fall into the prescribed agenda of USAID.
Despite their name, nonprofit organizations often have money to give away. For example, The Nature Conservancy has several billion dollars to allocate toward environmental conservation projects, whereas Do Something.org gives away $500 each week to kids with worthwhile projects who just need a bit of capital to get started. Larger nonprofits tend to have more money to give away, if they are grant-making nonprofits at all, so check with the most high-profile nonprofits in your field for the best odds of scoring some cash.
Companies and Corporations
With the growing importance of a company's environmental footprint, its perceived social responsibility depends in some part on its philanthropic activities. For you, the grant seeker, this is great. Corporations and companies large and small want to give away money that generates good publicity, so they'll tend to support activities in areas where they want their business to grow and also in communities where they are most well-known -- oftentimes near the factory or plant where the products are made. However, projects that are in line with an image or theme a company wants to associate itself with are often funded by the private sector, too. Many corporations have foundations through which they give, such as the Coca-Cola Foundation, the Walmart Foundation, and the GE Foundation.
Any stakeholder in the sector where you're working is worth investigating to see if they will give you money. Professional associations often support individuals starting a career in the profession or individuals who've achieved a noteworthy goal; local stores and businesses often support local sports teams or charities because of the extra exposure their sponsorship will generate in the local community; national boards such as the National Collegiate Athletic Association award grants to individuals who excel at the national level, while community organizations such as local Rotary, Chamber of Commerce, Lions, Elks, or Women's Clubs often give to local stars who can shine on a higher level with a little boost from the town's leaders. Last but not least, universities and affiliated fellowship programs are rich sources of grant money, and often have career centers or financial aid offices that can help you with your search. Good luck!