Yes, you can buy a house with no down payment.The government offers a few choices when it comes to zero down loan options, including VA loans, USDA Rural Development loans and subsidized loan programs. For more information about the different loans that require little to no money down, check out this article from Bankrate.com. 
If you are a single parent or a family with low income, you may also want to check out Habitat for Humanity. This nonprofit Christian housing program builds and renovates homes for people who have a steady income, are willing to put in sweat equity to help build their home and can make affordable monthly payments.
Additionally, if you can find a home that is listed below the appraised value, you may be able to use the difference between the selling price and the appraised value as a "down payment." For example, if you find a home that is listed for $100,000 and the home is actually valued at $120,000, the $20,000 in equity can be used as all or part of your down payment.
Finally, many lenders allow the seller to pay for most, if not all, of the closing costs. This can help you have the money needed for your down payment.