Do the math and the math will tell you what to do.
Let's assume you buy a $200k house (to keep math simple). You have 2 scenarios: First, you put the entire $100k down, second, you put 20%, $40k down. Let's assume the property rents for $2k, mortgage at 5%, and you have $500 in fixed costs (tax, insurance, etc.). In scenario #1, your mortgage is $540. In scenario #2 your mortgage is $860.
In scenario 1 (the full $100k down) you will cash flow $2000 - $500 - $540 = $960. Your CoC ROI will be (12 * 960) / 100,000 = 11.5%. In scenario 2 ($40 down) you will cash flow $2000 - $500 - $860 = $640. The ROI in case 2 is (12 * 640) / 40,000 = 19.2%. The 20% down scenario has a much higher ROI.
I chose the numbers above to keep the math simple. However, you will find that ROI is always higher with less down.
Now some folks will go crazy and start talking about 0% down and infinite ROI's! This is where you have to apply some common sense. You should put enough down that you will cash flow. And cash flow enough that you can handle repairs, maintenance and vacancies. (I like to assume 20% of rent price for these expenses.)
The cool thing is that you can run the numbers in the other direction. You can figure out what amount down you need to make the property cash flow. Then calculate the ROI based on this amount. Then you compare that calculated ROI against other investments. For example, lets say that the ROI on the property your looking at ends up being 8%. Well Patch of Land is offering 10% pretty regularly right now. It would probably be better to put the money in patch of land. (Make sense?)
Finally, going back to the original example, I want to point out that if you can find 2 houses for $200k each, and put 20% down on both of them, you will cash flow (2 * $640) = $1280 which is more than the $960 you would have made had you put the entire $100k down on just one of the houses. And you'll still have $20k of your original $100k left in your pocket. Which I think really illustrates why leveraging and using other peoples money is always the superior investment strategy.