The Fulbright Scholarship amount varies from country to country. As I mentioned elsewhere, the Fulbright Scholarships vary immensely depending on your country of origin. The information given here is for the grants for PhD students doing research in the USA.
The Fulbright scholars in the USA I’ve talked to got from $1200 to $2300 per month in 2010, depending on part of the USA they lived in. Apart from the grant, they usually get $350 to cover expenses during first days in the US, and a $1000 books-and-supplies allowance. In some cases, the round-trip international transportation from your home country to the USA will be covered by a home country source.