Are there really any grants out there that are legitimate? Are there any out there that really help you and really do send you a big check in the mail?

There are lots of grants available but they are rather specific in what they are to be used for and usually not intended for personal use! For instance I write many applications for grants for a charity that I work for. This may keep me in a job but the majority of the money goes on service delivery. So in this sense grants are available to community and voluntary groups as long as they are properly constituted, have a management committee and/or have the correct legal structure.

Grants are also available to scientists who have research to carry out or theories they want to develop. Of course the grant maker needs to believe these are valuable and worthwhile projects and won't give out grants willy nilly.

Grants are sometimes available to small businesses or start ups. If you are in the UK the best place to find out about these would be the business link website.

@Susana answered the first part well. As to big checks? Not from the federal government. The grants the feds dole out are paid via drawdown, that is a wire transfer with a lot of security protocols. And even then it is parsed out over the life of the grant and every penny has to be spent according to the grant proposal budget. Any deviation has to be approved by a contracting officer in charge of the grant.