There are 4 types of federal grants that do not have to be repaid. They are:

1. Federal Pell Grant - They are generally awarded only to undergraduate students.  The annual award can be anywhere from $400 to $4,310 and the amounts can change yearly. 
2. Federal Supplemental Educational Opportunity Grant (FSEOG) -FSEOGs are awarded to undergraudate students with exceptional financial need - those with the lowest Expected Family Contribution numbers.  Federal Pell Grant recipients receive priority for FSEOG awards.  FSEOG awards range from $100 to $4,000 per year and the amount is determined by your school's financial aid office.
3. Academic Competitveness Grant (ACG) - For undergraduates receiving Pell Grants who are U.S. citizens enrolled full-time in their first or second academic year of study.  For first academic year students who have completed a rigorous secondary school program of study, graduated from high school after Juan 1 and have not been previously enrolled in an undergraduate program.  For second-year students you must have at least a 3.0 grade point average as of the end of the first academic year of undergraduate study.  First academic year students can be awarded up to $750 and second academic year students can be awarded up to $1,300.  For a list of recognized rigorous programs of secondary school study in your state visit www.ed.gov/admins/finaid/about/ac-smart/state-programs.html 
4. National Science and Mathematics Access to Retain Talent Grant (National SMART Grant) is for undergraduates receiving Pell Grants who are U.S. citizens enrolled full-time in their third or fourth academic year of an eligible degree program majoring in physical, life, or computer sciences, engineering, technology, mathematics or critical-need foreign language and have at least a 3.0 cummulative GPA.  Annual Award is up to $4,000 for each of the thrid and fourth academic years. 

Source:  Funding Education Beyound High School, The Guide to Federal Student Aid (2008-2009)