Organizations like Academy Fellowship and the University & College Poetry Prizes are always looking for talented poets to help. Private grant programs also include the Lenore Marshall Poetry Prize and the James Laughlin Award.
Writers interested in imaginative stories should have a look at The Mystery Authors of America as well as the Poets & Writers Magazine grants. Fiction writing is a large market today, so grants are plentiful but competitive.
Writers looking to create educational works can look into grants like the Lannan Literary Grant and National Endowment for the Humanities.
Make sure you understand the demands of your grant organization. Each organization is different, so rules for one grant may not be the same for the other.
Unfortunately, plenty of grant scams exist to trick the eager author. Always thoroughly research any organizations offering grants through websites like the Better Business Bureau.