Valid passport
Make sure your passport is valid for at least six months beyond the expiration of your period of authorized stay in the U.S.
Valid visa stamp and potential delays
Unless you are Canadian and visa exempt, your visa stamp in your passport must be issued for the correct nonimmigrant visa classification and must be valid at the time of your planned reentry to the U.S. and must reflect your correct nonimmigrant visa status. If you have changed or extended your immigration status since your last admission to the U.S., you may need to apply for a new visa stamp in order to reenter the country. Please refer to the OVIS website for information about the visa application process. Keep in mind that this is an extremely busy time and there may be backlogs for visa appointments. The Department of State maintains information on visa wait times at the various posts around the world.
Valid Form I-20 (F-1 Students) or Form DS-2019 (J-1 Exchange Visitors)
Check your form to make sure you will reenter before the program end date, and that you have a valid travel signature from OVIS. The travel signature for F-1 and J-1 visa holders is valid for 12 months, unless you are a graduated F-1 student on OPT or STEM OPT, in which case your I-20 travel signature is valid for 6 months. To request a travel signature, see the instructions in the OVIS website. Note that the U.S. government has made permanent its policy allowing electronic signatures on Forms I-20 and Forms DS-2019. Students and scholars can use Forms I-20 and DS-2019 with an electronic signature from OVIS, or an electronically produced copy of a wet signature. Students and scholars MUST print out the Form I-20 or Form DS-2019, sign with wet signature, and carry the paper copy for presentation at a U.S. Consular appointment and when seeking admission to the U.S. at a U.S. port-of-entry.
Travel and OPT - While on OPT you are still considered to have F-1 (student) immigration status, even if you have completed your studies and have since graduated. You must carry the required documents listed here.
The SEVP policy can be found here.
The DOS policy can be found here.