Separation of 2 compounds ( Powder ) Suppose I have a mixture of 2 pure binary compounds, a white powder. What is the best method to separate the 2 compounds? 

What I have thought of so far is to dissolve powder in DI water and carry out filtration if one compound is soluble and the other is not. However, I have not been able to think of any other methods to separate the 2 compounds if both are either water-soluble or water-insoluble. I considered fractional distillation but the compounds may become anhydrous. Furthermore, the boiling points of the compounds are not given and they could end up being too close for fractional distillation to work.

Is there any efficient, and preferably simple, method to achieve the above-mentioned desired result?

Edit: Is there any general method of approach for separating such 2 compounds as there is for separating water-soluble and water-insoluble compounds?[Filtration]  Or does it have to be achieved purely by trial and error of various methods?
Your question is about as broad as chemistry itself. Like you said, you may try dissolving them in water, if one is soluble and the other is not. If it's not working with water, chances are it will work with ethanol, or acetone, or... see, there are many solvents on the shelf. No luck? Maybe by now you've found something that dissolves them both, so you may try fractional crystallization. Still no luck? Maybe the compounds differ in density or selective adhesion of something, so flotation might help. Still no luck? Chromatography, by any chance? No? Distillation, like you said (provided they both would survive until boiling point), or maybe sublimation (good for $\ce{NH4Cl + NaCl}$)? No? Well, there is a multitude of chemical processes; some of them might change (that is, destroy) one compound or both, but probably in such a way that they can be regenerated later.

And if everything else fails, you can always look at the mixture under a microscope and separate the crystals manually.