If you have placed a down payment on a car but have not sign any contract and you decide you don't want the car any more can you get your money back?

You should have a receipt for the deposit and you need to read the small print for any language regarding a refund of the deposit. It may or may not depend on the goodwill of the dealer and the period of time passed since you made the deposit..
Yes ... If you have not signed any papers (repeat ANY) ... hopefully they gave you a receipt for the money given as a down payment ... otherwise, you may be left holding the bag for any proof.