Why can't I update iMovie? I tried to update iMovie and got the following error.

Update Unavailable with This Apple ID
This update is not available for this Apple ID either because it was bought by a different user or the item was refunded or cancelled.

It is true that I have not purchased it, indeed I don't think I have ever used it. It came with my MacBook Pro when I bought it in 2011. I mainly decided to install to stop the App Store from nagging me about it.
EDIT
After a number of calls to Apple Support, and a solution which didn't work I was given a redemption code to install the new version.
If you're running a system prior to OS X 10.9, you might consider updating it. Upgrading Apple's iApps from the 2011 versions to the 2013 versions requires either Mavericks (for version 10.0.5) or Yosemite (v10.0.6). The boilerplate message from the App Store has misled a good number of people.

If, on the other hand, you are using 10.9 or 10.10, first check the "Purchases" page of the App Store (Fourth icon across on the top of the toolbar) to see if the iApps are available for download. These versions replace--not upgrade--pre-installed iApps with bundles which tie them to a combination of your Apple ID and your computer's hardware ID.

If such isn't the case, contact Apple Support for Mac Apps, and explain your situation. You are entitled to an upgrade.