There are several types of hydraulic pump commonly used in hydraulic systems. These include gear pumps, vane pumps, piston pumps, and axial piston pumps. Gear pumps are simple and cost-effective, vane pumps offer high efficiency, piston pumps provide high pressure capabilities, and axial piston pumps combine high pressure and efficiency for demanding applications. Each type has its own strengths and is selected based on specific system requirements.