There are a number of ways to buy without getting a new mortgage. It depends in part on what the seller needs and wants...level of motivation and what he/she needs. For instance, if someone's starting to fall behind on payments, or is worried about that, and if you can afford the payments, and the seller just wants to get out, you can purchase "Subject To" the existing mortgage.
If the owner is financially stable, but still wants out, you can do a lease-option or lease-purchase. Or, as some here advise, instead of using that, use a land trust (particularly a variation called the NEHTrust) to accomplish the same thing: property is transferred to a trustee; you lease the property from the trust, and ultimately the property is brought out of the trust and you refinance it.
And there are many other possibilities. Find another party to put up the down payment, and enter into an equity sharing arrangement with him/her. You and the other person would both be owners of the property and when you eventually sell, the other person--per the terms of the equity share agreement--would receive his investment back plus profit.
There are a lot of other ways, too. But that should start you off.
How sure are you that it's a really good deal? Did your agent do the comps? Many deals look great until you look at days on market (remember to check back many sellers have taken the home off the market for 60 days to get the days on market back to zero and if your Realtor doesn't do a background check you don't realize that the home was on the market for over a year befor that), condition of the home, location and the underlying factors that have prevented the home for selling which is why the seller is discounting the home now and the new buyer is then stuck with those issues later when they go to sell. Your Realtor will be able to do the comps and look at all the issues and concerns to help you determine how good a deal the good deal really is.
If your credit is really good, there are still a few 100% loans out there, but your credit has to be great (call me for lenders who are still doing 100% (those are disappearing fast) . If your credit isn't great, then have you considered offering the seller more money, but asking him to give you back money (a credit) toward your closing costs/prepaids, principal, points and interest?? All things your Realtor will take care of for you when the contract is written.
Above all, use a VERY reputable lender. You want to get to closing, not have someone who promises you the moon then at the last minute doens't deliver and you're left holding the bag. Your Realtor will have the names of reputable lenders that have done an excellent job for past clients (call me if you need names and numbers, I have excellent lenders that I work with who can close quickly)
Good luck! There is nothing more wonderful than buying your first home