This is an interesting question, because there is no simple answer - many different things are going on. A quick answer is that many materials don't exhibit clear melting points because heating turns them into something else before they can melt. Here are a couple of examples:
Generally, pure substances have simple, well-defined melting and boiling points. But there are many exceptions. A key example is gypsum - CaSO4 . 2H2O - calcium sulfate dihydrate. When it's heated, it first dehydrates in two steps. Initially it loses 1.5 of the water molecules as vapor, then in a second phase it loses the last 1/2 water molecule as vapor. When this dehydration is complete, the remaining compound is not the compound that we started with - it is now CaSO4. And if heating is continued, much of the CaSO4 will decompose - producing CaO (solid) and SO3 (vapor). Eventually, some melting will be observed, but the melted material will actually be a mixture of CaO and CaSO4.
There's a very detailed description here: http://nvlpubs.nist.gov/nistpubs/jres/27/jresv27n2p191_A1b.pdf
For more complicated materials, similar processes occur, though not always as predictable. Your last question was about wood. As wood heats up it first dries out as you stated - i.e. the free water within the wood boils and leaves as vapor (this is not chemically bound water as in the gypsum). Then as heating continues, the cellulose and other complex organic molecules thermally decompose, producing a lot of light organic compounds such as methane, butane, propane, alcohols, etc. These are essentially small bits of the molecules containing carbon, hydrogen, and oxygen which break off and float away. If oxygen is present, these will burn to produce more heat to speed up the decomposition process, but even without oxygen this decomposition will occur.
Eventually, no more light hydrocarbons can be released, and we are left with carbon and various trace elements including potassium, calcium, magnesium, etc.. This is charcoal. Continued heating can eventually get to the point where these materials melt, but what remains is no longer wood - it's carbon and a few other things - so there is no point at which "wood" will melt.