Using the trip delay benefit and dealing with interruptions

You're sitting in an airport, watching your flight status switch from "on time" to "delayed." Not the great start you were hoping for.

If you're an experienced traveller, you know that sinking feeling you get when a trip delay strands you. To protect yourself it is recommended that you purchase travel insurance that includes trip interruption and trip cancellation insurance. But how can insurance help, and when should you give up and cancel your trip?