I've been rewriting from scratch the framework for
my game. Recently I've been given much thought to how I want to layout the world.
My goal is to create a level and editor that has the same visual appeal of the indie games Limbo or Feist:

My question is how do you create more organic, realistic looking (2D) level such as that?
I imagine much of the a lot details are a freely placed "entity" based system, which I don't have an issue with. But what about the terrain in which the player walks on? It seems very smooth.
Before I was using a very strict tile-based system. Fixed size 2D array with corresponding tiles linearly drawn. I found it creates a very boxy result and I can't imagine using tiles to create a world like that. The curves just seem so much more natural than having a collection of variably angled tiles. I've even had freely placed images (rotation, scale, and position), but I'm not sure how to get the desired result using them. (for instance smooth collision across the top seems like it would be exceedingly difficult, even WITH the box2D implementation I have)
What methods are there to laying out a level that I'm missing? Is it a series of Polygons (where the mapper can move around vertices?) That seems like it would be unbearably hard to edit unless some clever methods were made that I'm unaware of.