Strictly speaking, you are supposed to pay taxes on any capital gain. In practice, when you sell a car for a few thousand, no one worries about it - sort of like Internet sales tax. But as our dear state shares more information between agencies like the DMV and the FTB, I'm sure the day will come when vehicle sellers will receive a notice of taxes due following a sale.
Not to hijack the thread, but selling cars privately is restricted to a small number per year, four or so, can't remember. Any more than the lightly enforced limit and you have to be licensed. If "they" started to collect capital gains on these types of sales they would also open the door for claiming losses.