Can a commercial pilot fly passengers for hire without an air carrier certificate?
If you are referring to the USA with the regulating body being the FAA, this link will give you your answer. All text below came from this site:
http://www.cfidarren.com/cpinfo.htm

Here is the answer I think you are looking for:


  If your customer approaches you, with his own airplane (either he rented it himself, or he owns it).  In this case you may fly for hire, because you are not offering your services as a package or "holding out" as a commercial operator -- air taxi or charter.




Answer details:


  Commercial Pilot Certificate
  
  A certificated Commercial Pilot is paid for services as a pilot, provided you meet the qualifications which apply to the type of operations you are doing.  Some of this flying is  controlled by Part 91, but most commercial flying is controlled by Part 119, 121, 125, 129, and 135.  
  
  Do I need a new medical certificate?   To exercise your commercial pilot privileges, you must get a new medical (at least 2nd class) every year.  If your 2nd class medical expires (and becomes a 3rd class), you cannot exercise the privileges of a commercial pilot. 
  
  What can I do with a commercial certificate?    The following are things commercial pilots can do under part 91 - 
  
  
  Local scenic flights within 25sm of departure airport.  
  Ferry Flights  
  Crop Dusting  
  Banner Towing  
  Aerial Photography  
  Fire fighting 
  Go on to earn your flight instructor certificate
  
  
  Can I fly people around for money?  You can certainly be paid for being a pilot with a Commercial Pilot Certificate.  You may work for an Air Carrier certificated under Parts 119, 135 or 121.  You may not be the Air Carrier conducting the business without getting an Air Carrier Certificate.  When you offer a package (airplane, price, pilot), you are no longer operating under Part 91 and would need an Air Carrier Certificate. An example would be "Can you fly me to Atlanta?"   If you provide the aircraft, you need to have an Air Taxi Commercial Operator certificate under Part 135.  There are different rules regarding maintenance, airworthiness requirements, crew member qualifications, and expanded VFR and IFR equipment lists that make Part 135 very different from Part 91.  
  
  So the answer is NO, you cannot fly people around for money.  A Commercial Pilot Certificate simply allows a pilot to be PIC engaged in a commercial operation (airline) that has an Air Carrier Certificate.  A pilot certificate does not entitle the holder to become a commercial air-taxi operator. 
  
  If your customer approaches you, with his own airplane (either he rented it himself, or he owns it).  In this case you may fly for hire, because you are not offering your services as a package or "holding out" as a commercial operator -- air taxi or charter.