Let me begin by saying that I don’t see any real value in buying a car new. You’d be better off waiting a year or two and buying the same model after the initial devaluation happens. If you insist, however, and you have to choose between a cash back rebate and 0% financing, here’s how it breaks down.
I’m taking liberties here and using a few assumptions. The first, and most important, assumption is that you’ll use the cash back rebate as an addition to your down payment. I’m also assuming a 5 year loan because that’s pretty standard for a new car loan. I’m assuming that you’re going to use the cash back rebate as an addition to your down payment, because you’d be an idiot not to. No really. Why would you buy a $20,000-$50,000 car that will lose at least 10% of it’s value the second you sign the dotted line and then also take the $2500 (Or however much) in cash? Also, if you do take it in cash, will you drop me a line? I’ve got some ocean front property in Oklahoma to sell you.
Assumptions aside, the deciding factor here is the interest rate. The lower the interest rate if you take the cash back, the better that side looks. Somewhere around 5.8% they are about even over the life of the loan. Of course, if you make extra payments that will change things as well. If you can get a rate of 4% or so, the difference is pretty good and you should use the cash back and run with it. At something like 8%, however, you’d be pretty silly to not take the 0% financing.
In the end, there are several variables that need to be taken into account such as trade in and sales tax. And this is far from a scientific study I did here, nor is it meant to detail exactly how to buy a car. What I would suggest is using a loan amortization calculator and punching in the numbers. For this little experiment, I used a calculator built for just such a calculation at interest.com.

Shane Ede is a business teacher and personal finance blogger. He holds dual Bachelors degrees in education and computer sciences, as well as a Masters Degree in educational technology. Shane is passionate about personal finance, literacy and helping others master their money. When he isn’t enjoying live music, Shane likes spending time with family, barbeque and meteorology.

I’d take the cash, use it as an additional down payment like you said, then make extra payments every month, like you said. I hate having debt, so I’d probably pay extra on the loan even if it was 0%, for example, I’m paying extra on my Best Buy debt right now, even though its at 0% for 18 months!
I’d … well, I’d never finance a car.
But if I HAD to finance a car, I’d do the cash-back option, because even if your interest rate is 0%, you’re required to have full-coverage insurance (that means insuring the full, non-depreciated value of the car) throughout the life of the loan.
Assuming you’d buy a cheaper insurance package when your loan is over … it adds to your incentive to get that loan paid off!
I would also take the cash and use that for the down payment.