If the computer is an asset owned by the organization, then yes, you should monitor employee computers in real time. Depending on your organization, you may want to monitor all activity on the computer with detailed screen capture capabilities or you may want to only monitor Internet activity.
The most common type of computer user activity monitoring, is internet browsing activity surveillance. Companies want to ensure that their employees are not visiting prohibited or malicious websites and putting their network infrastructure at risk. With the proper systems in place, these websites are blocked and inaccessible from within the organization’s network.
In addition to security benefits, organizations can control who has access (and when) to websites such as Facebook, YouTube, shopping, etc. This in turn maximizes productivity.
In determining your strategy for user surveillance and monitoring, you should consider company cultural respect and privacy. You should also speak to professionals to determine what you should monitor on a user’s computer.
Be aware of the laws that protect all parties. Below is some reference material: