It depends on the type of aircraft. Three and four-engined aircraft start with a limit of 180 minutes from a suitable airport. No matter the aircraft or operator, they can operate up to three hours flying time from a suitable airport.
Twin-engined aircraft, however, are subject to “ETOPS” restrictions. ETOPS is, officially, Extended Range Operation With Two-Engine Airplanes (or Extended Twin-engine OPS). Right now the farthest an ETOPS-approved aircraft can be from a suitable airport is 207 minutes (no-wind). The worst-case scenario would be an aircraft losing an engine at the most critical time, and then flying on one engine for 207 minutes until landing.
Why can ETOPS aircraft operate farther from an airport than non-ETOPS aircraft? Because of the reliability/accountability required. It requires provable engine and airframe reliability from both the engine manufacturer, airplane manufacturer and the operator.
ETOPS began almost 20 years ago with the Boeing 767-200ER. In order to be approved to fly trans-Atlantic with only two engines Boeing (and Pratt & Whitney) had to prove that the engines and airplane systems were reliable enough to allow such a flight. Before ETOPS twin-engine aircraft were limited to flying no farther than 60 minutes from a suitable airport. As ETOPS was introduced the time between airports for twin-engine aircraft steadily expanded to 120 minutes, then 180 minutes, and now to 207 minutes. ETOPS up to 240 minutes can be approved on a case-by-case basis.
The focus by engine manufacturers and airlines on reliability has produced some amazing results. In order to be approved for 180-minute ETOPS an airline must demonstrate an engine failure rate of less than .02 shutdowns per 1000 hours of flight time. In other words, for every 100,000 hours flown the airline can have no more than TWO in-flight engine shutdowns.
The result is VERY reliable motors on the twin-engined airliners being produced today.
Interestingly, most of the longer ETOPS requests do not come from flying over oceans, but from flying over the poles. Oceans have islands with inhabitants and runways. The Arctic has a whole lot of nothing for hours at a time.
And BTW, the “Unofficial” meaning of ETOPS?
Engines Turn Or People Swim.