The main thing to remember about your down payment is that it has to be "sourced" and "seasoned". What that means is the mortgage lender wants to verify that your down payment is coming from your funds and they want to see it in an institution for at least three months.
You will have to show three months bank statements. If you have $20,000 under your mattress, the guidelines will not allow you to use it for a down payment.
Exceptions to every rule right? Well, ... FHA guidelines will allow mattress money if you can prove that you do not use banks for checking or savings and that you operate on a cash only basis. (No credit either) Obviously this is very hard to believe in the world as we know it so it will be difficult at best to find a lender that will follow this guideline even if FHA says it is ok.
There are a few non-conforming loans that do not source or season the funds but they are hard to find in today's market. There are also programs that will allow a Gift for the down payment but those funds usually have to be sourced too. Oh, and the gift must be from a family member or a close friend. The lender will ask for their bank statements.
FHA requires 3.5% down unless you are using one of the Gift programs. (Still 3.5% if it is a gift) Closing cost may be paid by the seller and/or part of of the costs may be financed in the loan. The LTV can actually go as high as 97.75% If your credit score is below 580 you will have to put down 20%. Remember, the lender can require more even if FHA does not. They use credit score to determine how much is required. If your credit is good you shouldn't have anything to worry about.
VA has a Zero down program and closing cost can be paid by the seller.
Fannie Mae and Freddie Mac Require 5% down and sometimes they carry first time homebuyer programs that only require 3% down. Again, please remember that it is all credit score driven so you might not qualify for the minimum down payment.
It is still possible to get 100% financing in this market. Of course the interest rates are higher because the risk is higher and these programs are credit score driven. A score lower than 640 will usually require a down payment and the lower the score the larger the down payment.