Generally speaking, you should put down as much as you can afford to minimize the amount you are borrowing. This will save you interest over the life of the loan.
The caveat here is when you are borrowing in a low-interest-rate environment. With low interest rates, the savings you get from putting down more cash are lessened or nullified.
Conservative advisors suggest a down payment of at least 15% to 20% of the price of the car. This applies regardless of your credit score.
If you have a short credit history or a poor credit score, you may not be approved for a loan at all unless you put at least 10% down.