1. Most often noise comes from the wash pump. Either something is lodged in the pump blade or the pump motor bearings are bad. On some designs it is possible to service the pump and seal system without replacing the motor. A noisy motor must be replaced.
2. Many recent dishwashers have a separate pump. Debris may get caught there and make noise. Usually however this small motor just quits draining and hums quietly.
3. Very old dishwashers had a drying fan that can also make noise. This applies to KitchenAid and Maytag.
4. Soap dispensers can be noisy.
5. Bad hinges can make an awful squeek when the door is opened.
Clogged Pump