Trent at The Simple Dollar blog would rarely recommend getting into debt, but since financing a car is sometimes a necessary evil, he recommends taking a good look at your finances, and the market, before signing those dealership papers. He walks through familiarising yourself with your credit report, shopping around for loans, and, of course, saving early, but his key advice on how much to put down is summed up in one sentence:
Have at least a 20% down payment (unless you're buying an old car, then 10% is the bare minimum), but if the interest rate is over 7%, save for a bigger down payment and wait until you absolutely need the car.
Anyone's mileage will vary, depending on their finances, but Trent's advice seems pretty solid. How have you determined what you should and shouldn't put down on a new or used car? Share your own advice, and other car-buying tips, in the comments.