Will they take my house if I file bankruptcy? (Part 3)

In this Part 3 of the series "Will they take my house if I file bankruptcy?", the situation is that you're behind on your house mortgage payments, afraid they'll foreclose on your house, and probably in debt for other things. In this situation the question is better expressed as "Can I save my house by filing bankruptcy?". As with many questions about bankruptcy, the direct answer is a strong "it depends".