As long as you compensate properly and grant the required breaks, there aren't any federal limitations on how much overtime your employees can work.
The Fair Labor Standards Act (FLSA) doesn't place a limit on how much time an employee can work, so, in most states, the number of hours employees can work in a week is potentially up to the amount of hours in a week.
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State Law Exceptions
Illinois, New York, and Wisconsin have laws limiting the most days worked in a week at a single job to six, effectively safeguarding employees with one day of mandatory rest per week. But these laws don't limit the amount of hours that can be put in each day.
Other states have certain limitations in place. In California, employees can't be disciplined or fired for refusing to work more than 72 hours in a week. In Maine, an employer can't require workers to put in more than 80 hours of overtime in any consecutive 2 week period.
If you're mandating your employees put in overtime, it's advisable that you double-check your state's laws for any potential limitations.
Child labor laws limit the number of hours minors can work in a day.
A few regulated industries (i.e. truck drivers or airplane pilots) have maximum shift lengths.
Collective Bargaining Agreements arranged by some unionized occupations have created limits on the maximum hours they can be forced to work.
Although in many cases it's legal to require employees to work long overtime hours, it's generally not a good practice. The quality of employees' performance will likely plummet if they're feeling over worked. Also, jobs that are too demanding will likely have a high employee turnover rate.