It can vary by airline and even by flight (full flights may limit carry on), so you should check with your airline.
Typically, you will be allowed two pieces of checked luggage - each weighing no more than 50 pounds. If a piece weighs more than that, most airlines will charge a fee. Carry on is typically limited to one piece (that will fit in overhead or under the seat) plus a personal item such as a purse, briefcase or laptop computer.