Buying a house is not impossible if you have no money; you will just be subject to many other restrictions and fees. Don't get it wrong; you will end up paying that down payment back with interest. To buy a house with no money, you will eventually have to have money. But at least you have time, in the beginning, to work up some funds. Here's what to look out for if you're trying to buy a house with no money.
To buy a house with no money, familiarize yourself with Fannie Mae. This is the house lending program set up by the government with Freddie Mac to finance low income home buyers. Usually, if your FICO credit score is good enough, they will not require a down payment from you.
If you can get Fannie Mae to underwrite the loan for you, you still must remember closing costs, which is a huge chunk of money you will need on the closing date to buy a house. To buy a house with no money, truly, you must negotiate with the seller to pay closing costs, or else you will have to come up with that money. It is not something you negotiate with the loan originator.
To buy a house with no money, you should also look for seller homes, not bank owned homes or REOs, and you should look for single family homes, not condos or townhouses. Reason being: bank owned homes, REOs, short sales, foreclosures, and condos all have much more stringent requirements for money down than do single family, separate, seller sold homes. To buy a house with no money down means your options are limited, but there are still plenty. The best search site I've found is zillow.com.
If you can get closing costs paid for, make sure that your loan calculator factors in the PMI you will be paying every month because you are buying a house with no money down. PMI is a cool way to say "more money to the bank because you didn't put any money down at first." Now there are some arrangements in which as soon as you reach 20% equity by just paying mortgage payments, that PMI drops off. Work with your lender to make that happen.
No matter what, stay away from subprime mortgages. If you have no money down, and your income is shaky, if you get underwater, you'll just lose the house. Subprime mortgages might be illegal or frowned upon now, depending on when you read this, but they'll make a return. Stay away from them!