Personally, the more engines, the merrier!
I currently fly the 744 for a US carrier, mostly on trans-Pacific flights. In past lives I've flown both single- and twin-engine airplanes on long overwater operations.
The issue is simply one of redundancy and safety vs cost. If twin-engine airplanes were as safe as 3- or 4-engine airplanes, special ETOPS regulations would not be needed!
The issue goes beyond engines -- the twin has fewer electrical generators, hydraulic systems and pumps, and pressurization packs. In the 744, inflight shutdown of an engine is not necessarily a reportable emergency!
The issue also extends beyond ETOPS. When you lose an engine after takeoff in a twin, you lose 50% of your available power; with a 3- or 4-holer you lose 33% or 25%, respectively. While certification requirements will give the twin more excess power (and the requisite rudder authority) to begin with, performance over mountains (e.g., South America) will likely be more critical with twins.