What is the advantage of using a center tapped transformer in a full wave rectifier circuit?
Compare the following three configurations (from this document): 







Using the half wave configuration will require a transformer 78% higher current rating (and thus more expensive) for the same output current as well as twice the output filter capacitance compared to the center-tapped full wave configuration.  

An alternative (3rd configuration above) is the four-diode full-wave bridge, which uses the transformer even more efficiently (24% better than the center tapped and 2.2 times better than the half wave) but requires four diodes, and requires the same (smaller) filter capacitance as the center tapped configuration. 

However, it has a potentially huge efficiency hit for low output voltages because the diode drop is doubled (and so the diode losses), so the center-tapped configuration is often preferred (for example, in switching supplies).