On August 24, 2001, Capt. Robert Piche (a pilot for the Canadian charter airline Air Transat) did something that I would have (until now) flatly told you was impossible had it been proposed.
Air Transat Flight 236, an Airbus A330 twin-engined aircraft with 304 aboard, was in transit from Toronto to Lisbon on August 21st. The A330's ETOPS rating is 120 minutes. Over the Atlantic, the crew received a warning that the right engine had developed a fuel leak. It was shut down. At this point, the aircraft is theoretically able to fly on the remaining engine for the duration of its ETOPS (120 minutes); accordingly, the aircrew declared that they were diverting to Lajes airfield in the Azores islands, approximately 150 nm away.
There were further problems, however. The fuel leak was caused by a pipe breaking inside one of the Rolls-Royce Trent 700 series engines. This leak, which was caused by a low-pressure fuel line coming into contact with one of the hydraulic lines, ended up draining the entire fuel system, perhaps due to an improperly-acting weight and balance controller or valve. In any case, thirteen minutes after the right engine was shut down, the left engine experienced flame out from fuel starvation.
At the time this happened, the airplane was 65-85 nm north of its destination (and the nearest airfield), flying at 34,500 feet. When the second engine failed, generated electrical power was lost; hydraulics apparently continued to function, driven by the 'windmilling' fans of the left engine and their associated generator.
Capt. Piche and crew managed to fly the unpowered jetliner for 65 (some sources say 85+) nautical miles, and landed it at Lajes airfield on Terceira island. The landing blew eight of the ten tires on the airplane due to use of the emergency braking system, as the thrust reversers were unavailable and the airplane landed approximately 30 knots faster than its normal speed; however, it remained otherwise intact, and evacuation was complete within 90 seconds. Less than a dozen people were injured, all minor; most of those occurred during the evacuation.
Yes, you read that right; they apparently managed to glide a jetliner 65 miles. The fact that they were at 34,500 feet means that they knew what they were going to have to do; a fuel leak problem with one engine calls for the Airbus to move down to 15,000 feet or below so that outside pressure is high enough to prevent vapor lock in the fuel system which (presumably) has been compromised to outside air. The crew would have received notice of an impending imbalance in the fuel system on their left lower cockpit MFD in the form of a colored diagram of the fuel feed system appearing.
Even so, if we give them the benefit of a few thousand feet, they were at an altitude of approx. 6 miles. Traveling 85 miles means that (woohoo, math!) this particular A330 achieved a glide ratio of almost 11:1. For comparison, a Schweizer 2-33 - a standard two-seat training sailplane - has a glide ratio (gliders call it sink rate) of around 24:1. In other words, an unpowered, ultralight all-wing airplane designed for glide only did perhaps twice as well in distance. A Cessna 172 - a small high-wing general aviation aircraft often used for training, with a good glide ratio - gets 10:1 when trimmed for 'best glide,' according to its operating manual.
So, they knew they were running short of fuel; they climbed the airplane as much as they could before losing power (no doubt gaining as much airspeed as possible as well). Then they managed to glide in. Amazing.
According to records, the trip took approximately twenty minutes, which jibes well with the airplane's probable 'best glide' speed - ~215 kts - and the additional energy available from higher altitudes. Probably the most significant factor in their success was Capt. Piche's prior work experience - he had spent many of his 30 years flying time as a bush pilot, and as such, was an expert in dealing with air currents and emergencies sans runway. Still, they damn well better have given that whole flight crew a massive raise.
The story doesn't quite end there, however. The investigation that followed determined that Air Transat had been lax in its maintenance inspections; the air carrier was fined CDN $250,000 by Transport Canada, and their fleet's ETOPS ratings were capped at 90 minutes. The A330s in the fleet were dropped to 60 minutes.
'Pilot error' was cited as a leading cause of the incident, because the crew had carried out a FUEL IMBALANCE checklist from memory upon their first alert - that of a fuel imbalance between left and right wing tanks of over 7 tons. The reason this counts as pilot error is because that checklist contained a caution that if a fuel leak is suspected, the checklist procedure should not be used - however the crew, while having simulated a fuel imbalance problem many times, had never simulated it as a result of a fuel leak. Hence, their carrying out the procedure and allowing fuel to flow between the wing tanks allowed the full fuel load to reach the leak point and escape.
Because of their airmanship in responding to the crisis, the crew received a hero's welcome on their return to Canada anyhow.
The aircraft involved, tail number C-GITS, continued in service after repairs. Here is a video of it operating in 2012.