Can you get your money back on a car if you never took possession?

It depends on the details, but in general, no. Once you've signed a contract, you're bound by the terms of that contract. The fact that you didn't actually take the car is beside the point... you agreed to take the car, and signed legal documents stating so.

You should contact the car dealership as soon as possible. Depending on circumstances, they may be willing to let you out of your contract, even if they don't, legally speaking, have to do so.

One potential exception is if the reason you haven't taken possession is the dealership's (or manufacturer's) "fault". If you were promised the car would be ready Tuesday, and you signed the contract with that understanding, and here it is Wednesday and the car still isn't ready, you should contact a lawyer to see what your options are.