Kai Tak Airport was renowned for being difficult to land at. Surrounded by water, and with mountains on the approach, pilots were stretched to their abilities if conditions were not ideal. Several incidents occured where planes overshot their intended flight path.
1955 Vampire Crash. The Vampire crashed on September 6, 1955 after a training flight with a student on board. The plane had come in to land from the south-east via the sea on Runway 31 and overran the extension at the end and skidded into the nullah. (From Gwulo)
On 31 August 1988, the right outboard flap of a CAAC Airlines Hawker Siddeley Trident operating Flight 301 hit approach lights of runway 31 while landing under rain and fog. The right main landing gear then struck a lip and collapsed, causing the aircraft to run off the runway and slip into the harbour. 7 were killed. (From Wikipedia)
On 4 November 1993, a China Airlines Boeing 747-400, operating Flight 605, overran the runway while landing during a typhoon. The wind was gusting to gale force at the time. Despite the plane's unstable approach, the captain did not go around. It touched down more than 2/3 down the runway and was unable to stop before the runway ended. Although the aircraft ended up submerged beyond the end of the runway, there were only 23 minor injuries amongst the 396 passengers and crew. (From Wikipedia)
Here you can find another 'plane' buried in the ground around Kai Tak