As much as I am used to using autopilots when flying the airplane, I wouldn't recommend that you just trust it completely. I have personally seen an autopilot disconnect on an approach into an airport and it can be kind of scary. So after I had that happen, I keep a keen eye on all the automated systems when I fly.
This Video shows what can happen when a computer system malfunctions. This is an Airbus A320. Apparently the computer would not let the pilot throttle up after a low pass over the runway. Amazingly only 3 people on board were killed.
Here is a write up on what happened.
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