Situations, connected with aviation fuel can be extremely dangerous during the flight.
1. Fuel contamination.
Aviation fuel undergoes several tests before being put into an aircraft. Still it always contains little particles of water and some special chemicals to prevent it from freezing. During the wintertime possibility of fuel thickening gets much higher.
17.01.2008
British Airways Flight 38 was a scheduled flight operated by a British Airways Boeing 777 from Beijing which crash landed just short of the runway at its destination, London Heathrow Airport, on 17 January 2008. There were no fatalities but 47 people sustained injuries.

Although the fuel itself did not freeze, small quantities of water in the fuel did. Ice adhered to the inside of the fuel lines, probably where they run through the struts attaching the engines to the wings. This accumulation of ice had no effect on the flight until the final stages of the approach into Heathrow, when increased fuel flow and higher temperatures suddenly released it back into the fuel. This formed a slush of soft ice which flowed forward until it reached the FOHEs where it froze once again, causing a restriction in the flow of fuel to the engines.
The first symptoms of the fuel flow restriction were noticed by the flight crew at 220 m of height and 3.2 km of distance from touchdown, when the engines repeatedly failed to respond to a demand for increased thrust from the autothrottle. The autopilot disconnected at 46 m, as the co-pilot took manual control. Meanwhile, the captain reduced the flap setting from 30 degrees to 25 degrees in order to decrease the drag on the aircraft and stretch the glide. The plane landed on the grass approximately 270 metres short of runway 27L. The captain declared an emergency to the control tower a few seconds before landing.
During the impact and short ground roll, the nose gear collapsed, the right main gear separated from the aircraft penetrating the central fuel tank and cabin space, and the left main gear was pushed up through the wing. The aircraft came to rest on the threshold markings at the start of the runway. A significant amount of fuel leaked, but there was no fire.
2. Fuel starvation.
21.08.1963

23.07.1983

The subsequent investigation revealed company failures and a chain of human errors that combined to defeat built-in safeguards. Fuel loading was miscalculated due to a misunderstanding of the recently adopted metric system which replaced the imperial system. Instead of 22,300 kg of fuel, they had 22,300 pounds on board — 10,100 kg, about half the amount required to reach their destination.
24.08.2001

Leaving the gate in Toronto, the aircraft had 46.9 tonnes of fuel on board. 4 hours after departure, a cockpit warning system chimed and warned of low oil temperature and high oil pressure on engine #2. There was no obvious connection between an oil temperature or pressure problem and a fuel leak. Consequently Captain Piché, suspected they were false warnings.

Starting to realize they had the serious problem, the pilots decided to divert to Lajes Air Base in the Azores, declaring a fuel emergency. At 10000 m still 120 km from Lajes both engines flamed out and stopped because of fuel starvation.
The aircraft lost its main hydraulic power, which operates the flaps, alternate brakes, and spoilers. The descent rate of the plane was about 2,000 feet (600 metres) per minute. They calculated they had about 15 to 20 minutes left before they would be forced to ditch in the ocean. The air base was sighted a few minutes later. Captain Piché had to execute one 360 degree turn, and then a series of \»S\» turns, to dissipate excess altitude.
19 minutes later the plane touched down hard, at a speed of approximately 200 knots (370 km/h). Since they had lost the anti-skid and brake modulation systems, the eight main wheels locked up; its tires abraded and fully deflated within 450 feet (140 m). Fourteen passengers and two crew members suffered minor injuries, while two passengers suffered serious injuries during the evacuation of the aircraft. The plane suffered structural damage to the main landing gear and the lower fuselage.