You are advised to carry your passport and immigration documents (your I-20, DS-2019 or I-797 form) with you when traveling in the U.S. The documents will be required for a flight but could also be requested on trips where you are traveling by car, train or bus. For more information about the documentation required for air travel consult the guidelines of the Transportation Security Administration.
While it is extremely unlikely you would be questioned, having these documents with you provides immediate proof of your lawful status in the U.S. The Visa & Immigration Services Administration (VISA) office can verify this information by phone should that ever be necessary.