Example 1
The front desk clerk assured us that our hotel room would have a beautiful view of the Indian Ocean.
Since the Indian Ocean is getting twenty centimeters wider every year, ocean view rooms should be easier and easier to come by. Assured is the right word for this sentence because the clerk is making a guarantee.
Example 2
This policy will insure your car against accident, theft, and vandalism.
Does leaving the convertible top down in a thunderstorm because you got sidetracked by a Hotel Impossible marathon on TV count as an "accident"? We're asking for a friend. And in this sentence we're talking about the issuing of insurance, so insure is the correct word.
Example 3
I'm sorry, Miss. Just Jymnastics can't ensure your safety when you insist on doing triple backflips without a spotter.
Looks like this reckless gymnast just got schooled. And you'll get schooled, too, if you can't tell the difference between assure, ensure, and insure. Here, ensure is the right word for the job because it means guarantee.