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:

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.

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 preivous rovers, which make many methods not feasible:

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: