It sounds risky to operate with only 2 engines, and in 1953 twin engine planes were only allowed to be within 60 minutes of a diversion airport, mostly because of the unreliability of piston engines. It was a fairly long journey to allow twin engine planes to fly the kinds of routes they are allowed today. http://en.wikipedia.org/wiki/ETOPS
As jet engines turned out be much more reliable than their piston counterparts, the restrictions were loosened over time, starting with waiving the 60 minute rule for tri-jets in 1964. The original concept for the 777 was actually a tri-jet design. However the 767 turned out to be very reliable as a twin-engine plane and in 1985 it became the first twin engine plane to be allowed to fly 120 minutes away from a diversion airport (ETOPS-120) and in 1989 it was allowed to fly 180 minutes away from a diversion airport (but planes had to first complete 1 year with 120 minutes before they could be certified for ETOPS-180). Since twin engine designes were suddenly much more capable than anticipated Boeing dropped the tri-jet design of the 777, and eventually came back with a twin-engine design. By 1995 there was enough experience with operating twin engine planes with the 180 minute rule in place and Boeing was able to get the 777 certified to 180 minutes from the start.
So it basically took from 1953 to 1995 to allow a brand new twin-engine plane to fly most transoceanic routes (with a 180 minute rule in place), based on increasing evidence that the jet engines themselves are fairly safe, and learning more about additional safety mechanisms and procedures required to safely operate twin engine planes at extended distances from diversion airports.
As jet engines turned out be much more reliable than their piston counterparts, the restrictions were loosened over time, starting with waiving the 60 minute rule for tri-jets in 1964. The original concept for the 777 was actually a tri-jet design. However the 767 turned out to be very reliable as a twin-engine plane and in 1985 it became the first twin engine plane to be allowed to fly 120 minutes away from a diversion airport (ETOPS-120) and in 1989 it was allowed to fly 180 minutes away from a diversion airport (but planes had to first complete 1 year with 120 minutes before they could be certified for ETOPS-180). Since twin engine designes were suddenly much more capable than anticipated Boeing dropped the tri-jet design of the 777, and eventually came back with a twin-engine design. By 1995 there was enough experience with operating twin engine planes with the 180 minute rule in place and Boeing was able to get the 777 certified to 180 minutes from the start.
So it basically took from 1953 to 1995 to allow a brand new twin-engine plane to fly most transoceanic routes (with a 180 minute rule in place), based on increasing evidence that the jet engines themselves are fairly safe, and learning more about additional safety mechanisms and procedures required to safely operate twin engine planes at extended distances from diversion airports.