Seatbelts all the way!
All of our dogs wear a harness which connects to a short strap that snaps into the seatbelt clip. We got these "tethers" (as we call them) 10-12 years ago after I had an accident with my first dog, a chihuahua.
Carlos always sat on the front passenger seat on his blanket. One day I had to stop real short, and he ended up in a heap down by my feet at the pedals - there was no time to move him and I had to immediately shift back into gear to swerve around another car and I BROKE HIS TAIL when I slammed my foot onto the clutch to shift. I cried harder than he did! :( We went straight to the vet's office and got him patched up - he was only a few years old and had a kink in his tail for the rest of his life.
We don't take chances anymore - and I've convinced everyone in my family to do the same thing. Even my sister, who has a pickup truck, used to let her dogs ride unrestrained in the bed when the weather was nice. Now she attaches her dogs' harnesses to the tiedowns (each harness gets tied to opposite sides of the truck, so the dogs can't fall/climb out either side).
Here in NJ, as in most other states, seatbelts are mandatory for people and they have signs up everywhere that say "click it or ticket". Our babies deserve the same protection.