Passports issued in the United States expire 10 years after they are issued. Consider what would happen if you lost your passport or it was stolen from you, especially in a foreign country. Your passport number is just one key piece of information for you to have. Luckily, however, having to provide that passport number to officials is not a requirement when filing for a lost or stolen passport if you don't know it.
Locate the paperwork that came with your passport. There may have been a wallet-sized card that had your passport number on it as well as the number to the main federal passport issuance office.
The paperwork instructed you to sign your passport and make a few copies of the front page that has your picture on it and keep one copy in a safe place while giving the other copies to trusted friends or relatives. If you followed these instructions, then contact the friends or relatives that you gave copies to.
If you did not do any of the above, contact the travel agency you booked your last trip with. Your travel agent should be able to access your account and give you your passport number. If you made an online account with the agency, log in and search for the last itinerary you confirmed.
If you cannot locate your passport, the best thing to do is to report it lost or stolen by filing form DS-64 with the U.S. Department of State, Passport Services, Consular, Lost/Stolen Passport Section, 1111 19th St. NW, Suite 500, Washington, D.C., 20036. You can also call the State Travel Department at 1-877-487-2778 or go to http://travel.state.gov to do this. If you've lost the passport or it has been stolen, there is no fee for them to verify you had a passport previously issued.
If you are overseas, contact the nearest U.S. consulate or embassy. Always make copies of your passport to give to trusted friends or family before your departure. Carry a copy of your passport page with the photo on it separately from your person or luggage.
Once you report your passport lost or stolen, the number will be cancelled and you will not be able to use it. If anyone tries to use it going forward, authorities will be notified. If you find it, send it to the address above, and the cancellation can be removed. If you don't, the cancellation will remain in effect.