More than half (53%) of employees say their managers shouldn’t be able to view what they put on Facebook, Twitter and other social networking sites, according to a recent survey by Deloitte. For workers 18-34 years old, that number jumps to 63%.

But most managers disagree — 60% say they deserve to know what their reports do online. The main reason: Monitoring and protecting the company’s reputation. Social networking gives users a chance to make details of their lives public — and work is a heavily discussed topic. Browse any Facebook profile or Twitter account, and odds are you’ll find something about the person’s job.

Managers might have a real cause for concern: One-third of employees admit that they never consider how their employer will be affected when they post material online. Almost 75% admit that social networking sites make employers more vulnerable to damaged reputations.

What do you think — do supervisors have the right to check out employees’ online personalities? Do managers at your company search for folks on the Web? Let us know in the comments section below.