How many hydraulic systems does the Boeing 757 series have?
The Boeing 757 has three fully independent hydraulic systems. The three systems are "Left," "Center," and "Right." 


The left system is powered by an engine driven pump (EDP) on the left hand engine, an alternating circuit motor pump (ACMP) located in the wheel well, and a power transfer unit (PTU) powered by the right hydraulic system. 
The center system is powered by two ACMPs located just aft of the wheel well in the wing to body fairings, the center system can also be powered by a ram air turbine in an emergency. 
The right system is powered by an EDP on the right hand engine and an ACMP located in the wheel well. 


All three systems operate at a nominal pressure of 3000 psi.

Each system has its own reservoir. The reservoirs are air-on-oil type reservoirs and use engine bleed air to pressurize the fluid to provide proper head pressure for the pumps. The left and right reservoirs have a full fluid capacity of 6.6 gallons (on the ground), while the center reservoir is 3.5 gallons (on the ground). The reservoir itself is larger than these full volumes (roughly 50% larger) to allow for various effects, like thermal expansion of the fluid and different exchange volumes in actuators. 

In addition to the 2 EDPs, 4 ACMPs, 1 RAT, and 1 PTU, there are also two small electrical pumps in the left system that are used to unlock the uplocks on the landing gear for alternate extension. These pumps only function in flight when alternate extend is required, but they are also used to release the gear doors on the ground for maintenance using switches on the belly. 

Any one hydraulic system can fully control the aircraft, and further any one pump on any one hydraulic system can fully control the aircraft.

The image below gives a good block diagram of the 757 hydraulic systems. Another good resource for learning about the configuration of hydraulic systems on commercial aircraft is SAE AIR5005 "Aerospace - Commercial Aircraft Hydraulic Systems."