If we are talking about ionic substances there are no 'rules' for solubility, that is to say, one cannot deduce strict rules from patterns in the data. Solubility appears to be greater where there is a mismatch between the sizes of the ions, less where the ions are of approximately the same size. This must have something to do with the stability of the crystal structure which is being broken down as the salt dissolves. Even this sort of analysis does not explain all the data.

In organic substances solubility (in water) turns on the types and nature of the attached groups and secondarily on the length of the carbon chain. Polar groups attached increase the solubility, longer chains decrease it. Often the chain effect is very sharp, methanol and ethanol being completely soluble, propanol showing some reluctance and butanol considerable resistance to solution.

Try
http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch18/soluble.html
for a general run-down on this subject.

If you can find a copy of the New York State Regents Chemistry Refrence tables, they have a table in there. Otherwise, I'm sure that there are plenty of refrences on the web.

for ion-solubility in water another rule is, that solubility increases with the ionic character of the bond. If you have a bond with a strong covalent character it also takes energy for charge separation when you dissolve it to have single ions.

You get ionic bonds with covalent character if you put together an electronegative cation (noble metals: Ag+, Hg2+, ...) and an electropositive anion (S2-, I-, ...).