As the other answers note, the most common methods are: (1) short sale or (2) have the seller prepared to bring a check to closing for the balance owed.
There are several other techniques that investors use, but Realtors (for various reasons) aren't enthusiastic with them. In brief:
Subject To: The property is sold "subject to" the existing loan. Essentially, it's like the new buyer assuming a loan when it isn't assumable. This strategy violates the lender's "due on sale clause" but--especially in today's market--lenders usually are happy enough just to have the mortgage payments made on time.
Land Trust: There's a strategy used by some investors (real estate "guru" Bill Gatten refined the idea) in which the property is moved into a land trust. The buyer pays the full amount every month to the trustee (the owner), and the trustee disburses the money to the lender, taxing authority, etc. OR--the buyer may pay less than the full amount, with the seller kicking in a portion (maybe a few hundred dollars) every month. At some point, the property is brought out of the trust and sold, with the "buyer" having the first right to buy. For more information, go to http://www.landtrust.net
Hope that helps.