Causes

A code P0420 may mean that one or more of the following has happened:
Leaded fuel was used where unleaded was called for
A damaged or failed oxygen sensor (HO2S)
Downstream oxygen sensor (HO2S) wiring damaged or connected improperly
The engine coolant temperature sensor is not working properly
Damaged or leaking exhaust manifold / catalytic converter / muffler / exhaust pipe
Retarded spark timing
The oxygen sensors in front and behind the converter are reporting too similar of readings
Leaking fuel injector or high fuel pressure
Cylinder misfire
Oil contamination
Possible Solutions

Some suggested steps for troubleshooting a P0420 error code include:
Check for exhaust leaks at the manifold, pipes, catalytic converter. Repair as required.
Use a scope to diagnose the oxygen sensor operation (Tip: The oxygen sensor in front of the catalytic converter normally has a fluctuating waveform. The waveform of the sensor behind the converter should be more steady).
Inspect the downstream heated oxygen sensor (HO2S), replace if necessary
Replace the catalytic converter

Overall probably the biggest mistake vehicles owners make when they have a P0420 code is to simply replace an oxygen sensor (H02S). It is important to do proper diagnosis so you're not wasting money replacing parts unnecessarily.

We strongly recommend that if you need to replace the catalytic converter that you replace it with an OEM unit. Second choice would be a high-quality replacement part. There are many stories in our forums where folks replaced the cat with a cheaper aftermarket one only to have the code return shortly thereafter.

One thing to note is that many vehicle manufacturers offer a longer warranty on emissions-related parts. So if you have a newer car but it's out of it's bumper-to-bumper warranty, there still may be warranty on this type of problem. Many manufacturers give a five year, unlimited mileage warranty on these items. It's worth checking into.