What is the minimum number of engines required for taxiing an airliner?
Whether it's a twin-, tri-, or quad-jet, it very much depends on the aircraft design, airline policy, and conditions such as taxiway slope, contamination, weight, etc.
Read the below example for the Airbus A320 to get an idea:



An example of what can go wrong when taxiing on two out of four engines (or 1 out of 2) is having the aircraft in the wrong configuration. Like what happened on August 23, 2001 when the ground engineer had no steering or braking and they ended up in a ditch:


For the Airbus A380:


The minimum is a symmetrical two on the A380 (likewise for the 747).
777
In the 777 it is not allowed. That's an example of how it depends on the aircraft design.

Taxi – One Engine
Because of additional operational procedural requirements and crew workload, taxiing with an engine shut down is not allowed. High bypass engines require warm up prior to applying takeoff thrust and cool down prior to shutting down. If the engine has been shut down for several hours, it is desirable to operate at as low a thrust setting as practicable for several minutes prior to takeoff.
Note: Single engine taxi with an inoperative engine is authorized consistent with good judgement.
(Boeing 777 FCOM)


Fuel saving
According to this Eurocontrol document, the saving is about 4-8 kg of fuel per minute.