Employers typically can have hourly employees work on call. This means hourly employees may be required to stand by in case help is needed. The critical issue with hourly workers is when an employer is required to compensate them for on-call time.
On-call work for hourly employees isn't prohibited by the Fair Labor Standards Act, though some state laws have increased restrictions. Employers generally can have you work on call, such as in a customer service role or technician's job.
The factors that influence compensation are your location and freedom. If you are off-site and have significant freedom in your activities, a company doesn't normally have to compensate you for on-call time.
When you are on site, your employer is normally obligated by the FLSA to pay you, because you are restricted to be at the workplace. Also, if you are restricted in your movement or required to perform work-related activities, while on call, you are entitled to compensation. If on-call time puts you into overtime, you should receive time-and-a-half or whatever your state mandates for hourly worker overtime pay.