What could be causing my solid stained doors to make cracking noises?
One possibility is a slight cracking of the stain or finish coat on as sections of the doors as they expand and contract based on changes in temperature and/or humidity.  

Many doors have inset panels that are not rigidly glued in, but sit in channels in the rails (cross members) and stiles (upright members). When these doors are finished, the stain and finish coat may create a weak bond where these panels are joined. As the doors shirink and swell, the panels shift, breaking these seals.  There also may be a slight edge of finish that remains, and as the doors continue to shift, that edge may make noises even after the seal is broken.

One way to reduce dimensional changes is to make sure all six (6) faces of a door are sealed or painted. Often neglected are the top and bottom edges, and moisture can be absorbed through those raw faces increasing dimensional shift.