What problems led to the use of the Sky Crane system used by Curiosity?

Question

We all know about the fancy 'sky crane' system used on NASA's Curiosity rover.

The rockets slow the descent to 1 ½ mph and power a sideways parry to avoid the faster falling chute. As Sky Crane descends to 60 feet above Mars' surface, the rover inches down from underneath it on three nylon ropes like a spider spinning strands of its web. With Curiosity dangling 20 feet below, Sky Crane continues its downward progress until the rover is resting on the surface. Explosive bolts cut Curiosity's last physical attachments to the outside world, and Sky Crane flies away to death-plunge into the red sands, its incredible job done.

Why did they use this seemingly overly complex system? Why wasn't a simple airbag system used?

Answer 1

This NASA doc explains fairly clearly why the skycrane system was used:

Why not rockets, like the Viking missions?

"With a payload this size, the rockets could kick up enough dust to compromise the rover and its instruments," explains Sell. "And the rockets could excavate craters Curiosity would have to avoid as it drives away. Add to that the risk of a big, heavy vehicle driving down off the lander via an exit ramp to reach the surface."

How about airbags?

"Bags big enough to soften its landing would be too heavy or too costly to launch. Besides, you'd have to drop the payload so slowly for the bags to survive the load, you may as well place the rover right on its wheels."

This image really explains the difference in size between Curiosity and previous rovers, which make many methods not feasible:

Three Generations of Rovers with Crouching Engineers. Front: Sojourner, 1997; Left: Spirit/Opportunity, 2004; Right: Curiosity.

These are Earthbound prototypes. Curiosity had not yet been launched when this photo was taken.