Many cars manufactured by GM come with a security feature called the PASS-Key theft deterrent system. You can tell if a car has this feature by looking at the ignition key - the key's shaft has a small black module embedded in it with contacts on either side of the key. It is common to assume that there is some sort of chip or computer embedded in the key.
It turns out the system is a lot simpler than that, but still effective. What is embedded in the key is one precision resistor. When you insert the key in the ignition, the resistor becomes part of a simple circuit involving three other resistors. If the key does not have a resistor or it the resistor has the wrong value, the circuit disables part of the car's electrical system to prevent the car from starting.
So why is this system using something as mundane as a single resistor rather than some sort of sophisticated embedded computer? There are probably two reasons: 1) manufacturing cost, and 2) reliability. Number 2 is probably a very big part of the equation. Think about everything a key goes through - its typically riding in a pocket full of coins, getting thrown on the table, opening bottles, and so on. Keys have to be remarkable durable, they have to last the life of the car, and they must always work. If a system that depends on a single resistor can do a good job, then that's a good system to use because there is less to go wrong.
Why have the resistor at all? Don't the teeth on the key provide protection against theft? The resistor is simply adding a layer of difficulty to duplicating the key. It is fairly easy for a professional car thief to pick a lock or forge a key. By adding a component that is difficult to duplicate, you slow down criminals at least a little.
The following patent describes this type of system in a lot of detail: