I have used soft bike bags with success. However I was flying within Canada with Air Canada only, and would be a bit more weary if I was flying to places where the working conditions of ground crews are a bit more hectic...

I personally argue against the cardboard box. I think that because it looks like a box the bags guys may think that they can pile it up with other stuff, while in truth it definitely cannot resist the weight of a whole pile of bags and boxes in the cargo section of a plane. I was actually watching the guys loading our bikes into the cargo last time we flew with them (through the waiting area windows), and they were actually quite careful and carrying them as I would have, or better. The bags obviously cannot be placed at the bottom of any pile, they're too awkwardly shaped. Dunno what happened when they vanished outside of my view though. But the bikes camed unharmed.

Others have had a good experience with cardboard though, maybe they'll chime in.

When we packed our bags, we had cardboard squares attached to each wheel to further protect them (the bags are only lightly padded), the frames were wrapped with pipe-insulation foam tubes or bubble wrap, and the bags were generally filled with ziploc bags of clothes for further padding.

Don't forget to put spacers between your fork and rear triangle... (That's also true for boxes...)

Good luck!