Yes, it's possible.
You probably can't assume the loan. The loan probably is not assumable. However, there are half a dozen or so ways you can accomplish the same thing.
First, a disclaimer: I'm not a lawyer or an account. For professional advice in those areas, see a lawyer or an accountant.
Second: Recognize that the mortgage may be for more than the home is worth. So it might not be a good deal, financially, to take over the loan. Example: Owner bought the home 5 years ago for $500,000. He got a 100% loan, so he still owes close to $500,000. The home price has declined to $350,000. You'd be taking over a $500,000 debt on property worth only $350,000. There are times when that's the right decision, but more often it's not. So, be careful.
So, how do you do it? Lots of ways:
Subject To: You buy the home subject to the existing mortgage. The owner deeds the property to you. You promise the owner that you'll make the mortgage payments. That's it. Note: This technique violates the lender's due on sale clause, which says that the owner can't sell all or any part of the property without getting prior permission from the lender (unless the entire loan is repaid). Technically, if you violate the due on sale clause, the lender can foreclose. As a practical matter, that's unlikely. The lender would rather have someone--anyone--making full, regular payments on the existing mortgage than have to foreclose on the property.
Land Trust: The owner transfers the property into a land trust. He adds you as the resident beneficiary of the trust. So you own part of the trust, plus you're renting the property from the trust. You make your payments (often the amount of the mortgage--principle, interest, taxes, insurance) to a third-party trustee. The trustee, in turn, sends payment to the mortgage company. At some point in the future the property is brought out of the trust and you purchase it. A couple advantages to the land trust: If done properly, it doesn't violate the lender's due on sale clause. And as a beneficiary of the trust you can claim the tax deductions (interest, taxes) that a property owner could. For more information on those techniques, go to http://www.landtrust.net
In any case, make sure you have a good real estate lawyer assisting you. In the case of a land trust, make sure it's someone who really knows and understands land trusts; the folks at http://www.landtrust.net
can point you in the right direction.
Hope that helps.