Not necessarily, but safer to do so. I recently bought a used car from a private party, and we went to a lobby of a bank to close the final transaction. I got a cashier's check from the bank, signed it over to the seller, and exchanged the keys/title for the car.

This way, neither the buyer nor the seller needs to carry large amounts of cash with them. The cashier's check is not given unless the buyer's account has enough funds to cover it, so the seller doesn't need to worry about a bounced check.