Here in NZ we have what is called a Warrant of Fitness. It is also done annually, but not just on older cars. I've just got a brand new car, and it will still need a WoF next year.
The rules vary from state to state. All states have emission testing before you can register (tax) the car for a year.
After that every state has it's own set of rules for vehicle operation and safety standards. Most have yearly inspections for safety items such as tyres, glass, electrics, etc. while others do not, though they still hold the owner responsible for maintaining and keeping their vehicle in safe operating condition.