Yes there is a 14-Day Free Trial of LogMeIn Backup.
If you have not already created a LogMeIn Account for either the LogMeIn Free, LogMeIn Pro, or LogMeIn IT Reach software, you can begin the trial by clicking on the Products menu at the top of the page, and choosing LogMeIn Backup. Here you can click on the Get Free Trial box, and create your account.
If you already have an account with us using either LogMeIn Free, Pro, or IT Reach, log into your account while on the computer your wish to install LogMeIn Backup on. You can do this remotely if you already have LogMeIn Free or Pro installed on that corresponding computer. Click the Add Computer link on the right, choose LogMeIn Backup, and then the Trial option.
You can install up to 5 computers on a trial subscription.