If you need a passport in a hurry -- for a business trip or a vacation -- you can get expedited passport processing from the State Department or any of its regional passport agencies. (Remember, you still have to apply in person!) It will cost extra. There is a $60 fee per passport for this service in addition to your passport fee. For this fee, you get your passport issued, amended (say, if your name changes) and additional visa pages added as needed.
The State Department also strongly recommends that, if you use its expedited service, you also pay for two-way overnight mail for each application (you can pay this when you go to turn in your application, photos and fees). Passport applications sent together or at the same time do not necessarily remain together and will be mailed separately. So don't worry if a family member gets his passport back first. (Check details and payment methods of expedited passport service on the State Department's Web site.)
In ideal conditions, the passport agency processes expedited passports within three working days from receipt of the application. If you paid for overnight mail, you should receive your passport in about two weeks (if using the DS-11 and DS-82 passport application forms). You can also expedite passport renewal-and you can do it by mail.
If you need a passport for a trip that's starting in less than 14 days, you'll need to make an appointment at a regional passport agency (877-4USA-PPT) and bring along proof of travel. You can also use a private rush service, which can procure passports in 24 hours.