In Germany at least cars are checked and licenced by TUEV at regular intervals and after tuning (but not after servicing?). The owner has to pay for the check up, too, if I remember correctly.
In the United States this is up to the individual state, but typically you have to have a once-yearly inspection of your car. Some states will check that various parts of your car are in good working order, others basically want you to not have a check engine light on or be spewing too many fumes. There's no responsibility to even notify anybody that you or someone else has modified your car and there's no problem as long as the modification itself isn't illegal (even then people sometimes just pay the tickets and keep driving around with illegal modifications).
I spent a year in Japan and the contrast between Japan in the US as far as the average age/condition of cars you see on the road is quite striking.
I spent a year in Japan and the contrast between Japan in the US as far as the average age/condition of cars you see on the road is quite striking.