I'm actually quite surprised that this isn't really mentioned anywhere on the internet (or I'm just bad at searching)! Solubility in water is known to be directly related by multiple factors, and for organic molecules it's usually ability to form hydrogen bonds, polarity, bulk etc. I would imagine this trend would continue for most of the smaller alcohols (methanol, ethanol, isopropanol etc.) to some extent. However, I can't find even a brief mention on how solubility in common solvents is determined.
Let me share my (admittedly very elementary) logic: For a solvent like cyclohexane, which is non-polar, I imagine other non-polar solutes would be able to dissolve. However, if the non-polar compound is solid, it will require heating to break the van der Waals forces first. I assume little to no enthalpy change occurs in this process. Other more polar solutes would prefer to continue associating with themselves, and therefore not dissolve.
For a solvent like diethyl ether, it gets a tad more complicated. The oxygen atom on the ether is a hydrogen bond acceptor, and the molecule is polar. So, I imagine that non-polar solutes are poorly soluble. The same should go for compounds like amines, alcohols and carboxylic acids because they rather hydrogen bond with themselves. However, for meekly polar compounds with functional groups like aldehydes, ketones and halogenoalkanes, I imagine it depends on its polarity? It's polarity should be near that of the solvent; if it's more polar it will rather be with itself, if it's less polar the solvent would rather be with itself. So for example, if I mix ethyl chloride with diethyl ether, will they be miscible?