As little as possible is often the most popular idea.
However, it is wise to put down enough to make sure the property income will service the debt payments and taxes. You don't want to be paying out of pocket every month unless you really need the loss for tax purposes.
Most banks or savings and loans will require between 20 and 30 percent down payment in the US.
The lenders are looking for the property to break-even or have some positive cash flow based on their projections income and expenses.
The appraiser is often asked to make these estimates. However, I have purchased investment property with nothing but closing costs out of pocket using hard money lenders. I've even borrowed more than the purchase price when the appraised value was much higher than the purchase price.
I have also run across some credit unions that loaned 100% for borrowers who had a good track record with the credit union. It's all in the deal.