Apparently anything up to 35,786Km (22,236 miles) long!
NASA have offered a $2 million award to the team that can create a cable strong enough to support a space elevator rising from the equator to a ‘counter weight’ tethered in orbit more than 35,000 Km above the ground, using inertia to keep the cable taut.
So far no one has claimed the prize – The NASA team working on this idea believe carbon nanotubes may provide the answer but the technical problems are immense. To read more see: http://science.nasa.gov/science-news/science-at-nasa/2000/ast07sep_1/
So the next time someone on your team asks ‘How long is a piece of string?’ you have a plausible maximum value – the current safe answer is probably less than 35,000Km (but only until some genius rises to the challenge set by NASA).