Depending on the country someone will be driving your dog in, some laws may be in effect about this topic. The best way to know is to ask your vet about this.
For example, here in France, you have to make sure that the dog will, in no circumstance, be able to reach the driver if sitting on the backseat. So a net is in order if you are not using the belt.
Here is the "kit" I'd suggest:
- Buckle-leash: It is a simple small leash that has a buckle instead of a loop at the end. Note that most brands fit all cars but Volvo.
- Harness: You could buckle your dog using the collar, but might hang him if something happens. Also, a harness tends to calm the anxious dogs.
- Some rubber/Teflon sheet that holds onto the 4 head rests of the car. Teflon makes it a little bit more pricey but easier to wash and dry. The rubber part makes sure that it is not slippery.
I did not use a sheet until recently. The only reason we decided to get it is because the dog started to love swimming... Enough said :) But since then, he has an easier time staying in place, before he would slip a bit.
Note: the sheet we got required some small modification for us to be able to pass the seatbelt through. But it prevents the dog from reaching the driver so the belt was really just for the dog's safety.
The sheet I am trying to refer to:
EDIT: Coming back to this question/answer after a while I do realize that not enough emphasis was put on the fact that the safety of your car should be your last concern after taking care of the driver's safety, other occupants safety, and dog safety. A driver getting his elbow pushed by the dog who's asking for a scratch may become the cause of an accident...