In reply to neuromancer:
Never entirely easy to define, but Nanga Parbat's the mountain usually quoted in that regard -
"To the south, Nanga Parbat boasts what is often referred to as the highest mountain face in the world: the Rupal Face rises 4,600 m (15,090 ft) above its base. To the north, the complex, somewhat more gently sloped Rakhiot Flank rises 7,000 m (22,966 ft) from the Indus River valley to the summit in just 25 km (16 mi), one of the 10 greatest elevation gains in so short a distance on Earth." [Wikipedia]