While I buy cars in cash, my rule is you should be ABLE to buy the car in cash. In fact, you should be able to buy the car in cash, crash it and buy another one just like it.
If you find creative financing that lets you earn more: good for you.
But, if you're financing through the dealer, be very prepared for mathematical olympics. Every dealer I've dealt with used the old 4 square system (trade-in, purchase price, down payment, monthly payment). They scribble numbers down, talk to their manager, come back, scribble more.... I've seen more than a few people negotiate a price for a car, then add financing in there and -- with some scribbling and slight of hand -- end up paying more to get a low rate. These guys do this all day every day. For them, it can be like 3 card Monte.
The advantage of paying cash is: there is only one square. If you find financing elsewhere before you walk in to the dealer, that also takes you back to one square.