Why is it that NaCl dissolves so well in water but many other ionic compounds do not?

It all depends on the ionic compound you are trying to dissolve in the water. There are several rules for this thing, called solubility rules.

For example, Sodium Chloride is soluble because all 1A compounds (compounds with metals from the 1A column) are soluble in water.

There are other solubility laws at this website. I think you will find it very helpful when trying to determine what does and does not dissolve in water.

http://www.files.chem.vt.edu/RVGS/ACT/notes/solubility_rules.html