Great thread really, after reading through all of the comments and replies. I never thought about paying with a credit card, what a great way to earn bonus points and rewards. I'm not sure many dealers would actually do this though, for the reasons provided.
When we bought our two cars a few years back, we financed since we were just our of high school. Luckily, I had stellar credit for being 18 and, if I can remember correctly, got under 5.5% APR on each vehicle. my occupation treated me well too, and both card were paid off in one years time. With the financing, I went into the dealership with a check cut from the back on both vehicles, it was all too easy. Of course we had to get to an out the door price before I got my bank to mail me a check for the dealership, however, we were dealing with someone whom my family has been buying cars from for over 10 years. He wanted the business, and I wanted to help him in the process of getting some vehicles.
I think next time I go for a purchase, I'm swinging for the CC method and then cash (IE: Check) for the rest of the amount.