The main thing to remember here is that your down payment has to be "sourced" and "seasoned". What that means is the lender wants to verify that it is indeed 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 you cannot use it for a down payment.

Exceptions to every rule right? Well, FHA will allow mattress money if you can prove that you do not use banks for checking and savings and operate on a cash only basis. (No credit either) There are also a few non-conforming loans that do not source or season the funds. AND, of course there are programs that allow Gifts for down payments but those funds usually have to be sourced too.

FHA:
Requires 3% down payment unless you are using one of the Gift programs. (Still 3% if it is a gift) Closing cost may be paid by the seller and/or part of them may be financed in the loan. The LTV can actually go as high as 97.75%

VA:
Zero down payment, and closing cost can be paid by the seller.

Conventional:
Fannie Mae and Freddie Mac Require 5% down and sometimes they carry first time homebuyer programs that only require 3% down.

Non-Conforming:
It is quite common to get 100% financing in this market. Some lenders have more than 100% financing. Of course rates are higher because the risk is higher, and these programs are credit score driven. A score lower than 580-600 will usually require a down payment and the lower the score the larger the down payment.