Typically you still have to declare the "market" value and pay tax. I've seen people write a lower price on the bill of sale but that carries other risks (for example if the deal goes south, you have recourse only to the extent of the bill of sale value).
Usually not worth the risk for a few hundred bucks.
Like DireWolfM14 mentioned, there are states without sales tax but registering a car there usually requires proof of residence, which also costs money to fake.
In the end you're saving like $800 on a $10000 used car... for most people it's not worth the hassle and the criminal repercussions.
And all that is applicable only to person-to-person sales, which is probably like 1% of car sales in the US. Dealerships will roll the tax into your 10-year loan along with $50k of negative equity from the previous vehicle and off you go