What is producing the characteristic helix shape of the DNA?

Answer 1

Physics.

It's kind of difficult to be more specific than that, because there really isn't one single thing that causes it. It has to do with hydrogen bond formation, characteristic bond lengths and angles, the relative repulsion of highly charged ions, overlap of the pi clouds in the aromatic rings of the bases ... the double helix manages to satisfy all those conditions while creating a local minimum in the energy.

Now, there could be other shapes that satisfy the conditions -- in fact, there are at least three known naturally occuring helix forms that do so; these are called A-DNA (which adds a bit of a curve to the helix itself and is found particularly in dehydrated samples), B-DNA (the "normal" one), and Z-DNA (which twists the other way). For that matter, there are over 20 known forms, most of which only occur in the laboratory with a bit of artificial "prodding" such as methylating certain sites in the molecule.