As Maggie suggests, FHA probably is the first option to consider. If you're a veteran, consider a VA loan--that's 100% financing.
Or ask for seller assistance with closing costs. Rather than making an offer of, say, $300,000, you make an offer of $300,000 with the seller contributing $9,000 to closing costs. Or--if the appraisal will support it--offer $309,000 with the seller contributing $9,000 to closing costs. That can knock up to 3% off your expenses.
Or look at creative financing options--owner financing, for instance. Or lease-purchase, land contract, contract for deed, lease-option, and so on. In those, you won't get immediate ownership, but you will (generally) lock in a price and a time frame in which to complete the transaction.
Or find a seller willing to sell "subject to" (also called "Sub 2") the existing mortgage. Not too many will, but some do. In this case, the seller deeds the property to you. You, in turn, make the mortgage payments. At some point in the future, you refinance, removing the mortgage from the seller's name.
Or find an investor and do an equity-sharing arrangement. The seller puts up some cash in return for partial ownership in the property.
There are plenty of other ways, too. But those may provide you some starting points.
Hope that helps.