National Science Foundation Graduate Research Fellowship Program (GRFP). This is an incredibly prestigious award that provides significant financial support.
Interested students should begin at the applicant information page http://www.nsfgrfp.org .
The GRFP supports outstanding graduate students in NSF-supported science, technology, engineering, and mathematics disciplines who are pursuing research-based master’s and doctoral degrees at accredited United States institutions. The program provides up to three years of graduate education support, including an annual $34,000 stipend.
US citizens and permanent residents who are planning to enter graduate school in fall 2020 are eligible (as are those in the first two years of such a graduate program, or who are returning to graduate school after being out for two or more years).
The program solicitation (http://www.nsf.gov/funding/pgm_summ.jsp?pims_id=6201 ) contains full details. Note the different deadlines based upon field of study. Generally applications are due the 3rd-4th week of October.
This is a highly competitive program, and the application process is involved, so start early if you plan to apply.