Assure means (1) to inform positively, and (2) to cause to be sure. Ensure means to make sure or certain. And insure means (1) to provide insurance for, and (2) to have insurance for.
In British English, assurance was once the preferred term for some varieties of what we now called insurance. Insurance is now preferred, though assurance lives on in some company names.
English
In modern English, insure has no standard definitions unrelated to insurance, so this use of insure is questionable:
To insure that regular checks occur, the department installed electronic checkpoints with bar codes around the jail … [LA Times]
And these writers use insure well:
At $243, Allstate was the cheapest, but they wanted an extra $95 a year to insure the piano. [Wall Street Journal]
It said it would not have insured the securities on the agreed-upon terms had it known how the loans were made. [Reuters]
These writers correctly use ensure to mean make sure:
Working together as a team and under Red’s direction, we will ensure that this project will make all Texans very proud and will benefit our great state. [quoted. in NYT]
President Barack Obama said on Wednesday he would fight to ensure U.S. exporters had a level playing field to compete for world trade … [Reuters]
And here’s an example of assure used well:
Officials scrambled to assure Pakistan that the administration doesn’t condone the leak of 76,000 Afghan war documents by Web site WikiLeaks … [WSJ]
Assure is often used where ensure might make more sense—for example:
The way he frames the challenges facing the budget pretty much assure that conclusion. [The Heritage Foundation]
Periodic meetings of the chairpersons of all of these district evaluation teams in the state should occasionally hold meetings to assure that everyone involved understands what is expected of them and are operating accordingly. [The Baltimore Sun]

