I have often seen this extremely important question arise as a result of what I believe to be unclear instructions and explanations given to individuals when they present themselves at U.S. Consulates or at ports of entries such as airports when entering the U.S. The misunderstanding arises when individuals believe that the validity dates indicated on their visa, which they obtained from the U.S. consulate, controls how long they are allowed to remain in the U.S. In actually the date stamped and written on your I-94, which is the white document stapled in your passport when you actually enter the U.S., is what controls how long you are authorized to remain. Here are some further details:
Visa Stamp: The visa stamp that is placed in a your passport merely evidences that you have been to the U.S. Consulate or Embassy and have been determined by a consular officer to be eligible for the specific visa and may now seek entry into the U.S. Having such a visa DOES NOT guarantee that the Department of Homeland Security will allow you to enter once you present yourself at the Port of Entry with the visa. Further, the dates provided on the visa merely show how long you have to present yourself at the Port of Entry into the U.S. to request admission. Note that the visa may allow multiple entries in certain cases and may be valid for up to 10 years as is sometimes seen with visitor visas.
I-94: Once you present yourself for inspection at a U.S. Port of Entry using your visa, and assuming you are granted entry, you will receive an I-94 card in your passport which will indicate the visa status you have been allowed entry on as well as how long you are being admitted for. It is this date that determines the length of stay you have been granted and NOT the date on your visa stamp.
Example: Once you are issued a 10 year visitor visa at the Consulate and have received the visa stamp in your passport you take a flight to San Francisco and present yourself for inspection to the officer who asks to see your passport and visa. Assuming you are granted admission the officer will then provide you with an I-94 and a date indicated thereon. Normally as a visitor you will have a date covering a 6 months stay. What this means is that you are then allowed to remain in the U.S. for those 6 months as indicated on your I-94 and not for 10 years as indicated on your visa stamp.