Do Polar Bonds Affect Molecular Shape? Repulsion between shared electron pairs shapes the molecule in such a
  way that enables the pairs to be as far apart as possible. 
  Furthermore, the repulsion between shared and unshared pairs forces
  bonded pairs closer to one another.  These principles of the VSEPR
  theory and orbital hybridization, in addition to Van der Waals
  forces, explain the overall shape of a molecule.


In my textbook,  however, there was little mention to how polar bonds and the partial charges they cause affect the structure of a molecule.  I would expect that poles of the same charge would repel each other and have a profound affect on molecular shape.  However, many compounds make me second guess this assumption, including $\ce{H2O}$.

Do polar bonds at all affect molecular shape? Why or why not?  If so, to what extent?
Yes, of course they affect the shape. But only slightly so. More precisely, bond angles can change, however this does not change the general shape predicted by VSEPR.

For example, if two atoms (one with a positive pole, and one with a negative pole)  are connected by another atom, then the two atoms would make an angle that is smaller than the angle predicted by VSEPR. 

And also, polar bonds are capable of intramolecular bonding. Such as in protein-folding.  So they definitely contribute to molecular shape.