I have a Trane 900 with heat pump. The outside unit still runs even when I turn thermostat off. I have to shut it off from the breaker. I put in a new Honeywell thermostat and it still does the same thing. What's wrong?

Try shutting of the inside unit and what happens?
If it shuts down it may be a low voltage wiring problem or thermostat/wiring?
If it doesn't shut down, contacts on compressor may be fused together.