the bridge rectifier
The bridge rectifier is the full-wave rectifier most supplies actually use. It pulls both halves of the AC right-side up with four diodes arranged in a diamond, and — unlike the centre-tap version — it needs no special transformer, just any AC source across two corners.
Picture the four diodes as a diamond with the AC fed into the left and right corners and the DC taken from the top and bottom. On each half-cycle, two diodes that point 'with' the current conduct and the other two block, and the cleverness is that the load always sees current entering the same terminal regardless of which way the AC is swinging. So both halves come out positive, at twice the line frequency, just like the centre-tap circuit.
The trade-off versus the centre-tap design is that current always flows through TWO diodes in series, so you lose about 1.4 V (two drops) instead of 0.7 V. That extra loss and heat is the cost of dropping the centre-tapped transformer. Bridges are sold as cheap four-pin packages, and with a reservoir capacitor on the output they form the front end of the vast majority of mains power supplies.
Across a 12 V RMS (~17 V peak) AC source, a bridge delivers humps peaking at ~17 - 1.4 = 15.6 V (two diode drops) at twice the line frequency. Add a big capacitor and you have rough DC ready for a regulator.
A bridge: four diodes, two drops, full-wave DC from any AC source.
In a bridge, neither DC output terminal connects directly to an AC input terminal, so you cannot share a common ground between the raw AC and the DC. Its two-diode drop also makes a bridge wasteful at very low output voltages, where a single-drop scheme (centre-tap or a synchronous rectifier) wins.