9. The Satan Pit
In this episode, the second in a two-parter featuring the Tenth Doctor (David Tennant) and companion Rose Tyler, the Doctor and Rose find themselves on a planet at the edge of a black hole with some sort of beast buried deep in the planet's core.
When He Should Have Regenerated: The Doctor and scientist Ida Scott are trapped 10 miles beneath the planet's surface. They use a snapped lift cable to lower the Doctor a giant pit they find, where "the Beast" is presumably hiding. When they run out of cable, the Doctor makes the choice to unharness himself and fall to the bottom, in case he survives. The Doctor makes a point to say that he could survive a 30 foot fall, but the viewer witness him falling so far into the black pit that he becomes a speck, indicating a much further (and unsurvivable) drop. When we see him next, he is at the bottom of the pit, with his space suit visor shattered but otherwise unharmed. The air is breathable down in the pit, despite not being so at the surface or in the cavern, and the Doctor surmises that the air cushioned his fall. However, seeing as the Doctor and Ida seemed to be experiencing similar, if not identical, gravity to Earth when they were in together in the cavern before the Doctor's descent, there really isn't any way whatsoever that the Doctor shouldn't have regenerated upon impact.