We usually don't try to identify an unknown substances purely on the basis of these properties, but nevertheless they can serve to confirm the identification. For example, if we have an unknow organic substance with a melting point of 91oC, that alone is not much use because literally thousands of compounds have melting points around 91o, give or take a few degrees. What we would do in the old days is make organic "derivatives" of the compound and take their melting points. If we have the compound's original melting point, plus those of say three different derivatives, then we have a very good chance of identifying it using a standard handbook of such data, if the compound is listed. If not, we do what we normally do nowadays to identify new organic compounds, examine the infrared (IR) spectrum, proton and carbon-13 NMR spectra, mass spectrum, and perhaps other instrumental data to make the identification.
For ionic compounds, we would identify the cation and anion, using either standard chemical tests (the qualitative analyses students often do in general chemistry lab) or using more modern instrumental tests such as atomic absorption (AA) for metal cations, for example. Atomic absorption spectroscopy could be used to identify the metal(s) and their amounts in a solid metal sample as well, or perhaps an ore sample, after appropriate sample preparation. There are other standard instrumental methods in common use in labs used by agencies such as the Environmental Protection Agency to determine the identities and amounts of organic and inorganic substances in water supplies such as lakes and rivers and air, soil, and water samples collected from a variety of sources.
I've used conductivity to determine the concentration of ions in solution, but not to identify the ions specifically. I've never tested the conductivities of solid materials so I don't know how useful it is for identification purposes. Solubility information can be useful in cases where you can compare the solubility of the compound with solubilites of known compounds, but by itself solubility is about as useful as the melting point, not enough to make a certain identification unless you have only a very narrow range of possibilities to check for.
So in summary, some of the properties you mentioned are routinely reported in the chemical literature describing newly discovered compounds, especially the melting point for solid organic substances, but this is more of a formality rather than an ironclad means of identification. For the latter we rely on more specific chemical and/or instrumental methods.
Hope this answered your question somewhat! This is the field of analytical chemistry - quantitaive (how much?) and qualitative (what is it?) analysis. Feel free to ask further questions. You also might want to try Jim over at the The Alchemists Corner - I believe he is an analytical chemist by profession, so he will know a lot more about this field than I do. Good Luck!
Steve
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