Depends on the aircraft and the type of service it is operated in. Short haul regional jets will do as many as 6-8 short hops per day, while domestic long haul, like from JFK to LAX may only do 2 flights. International flights, like LA to Tokyo may only run one flight per day.
Aircraft with pressurized cabins are usually limited to a specific number of cycles (take-off, cruise, landing) before they must be retired. Non-pressurized aircraft can fly as long as the owner/operator wants to keep up with proper maintenance.
Most commercial airlines will run their aircraft at least 6 days per week, and 48 weeks a year. (given an average of 4 weeks per year down for maintenance) If a long-haul 747 flies 6,000 miles per day, you can do the math.
I am a licensed aircraft mechanic (A&P)