Are there any other substances that have no melting point, such as glass?

Paper springs immediately to mind. Application of heat doesn't melt the paper. Instead, a chemcal process changes the structure of the paper.

Wood is a weird example, because it burns, but a melting reaction does take place. The only one I could think of is glass, because it boils, but never really 'melts' per se...

OK, how about Carbon Dioxide, a solid that passes directly to a gas when heated?

What is the melt reaction with wood?

Have a look at this link:

http://www.physlink.com/Education/AskExperts/ae531.cfm

Carbon Dioxide is a good one, thankyou. The melt reaction with wood has something to do with how it loses shape intermittently between being hot and bursting into flames.

Carbon dioxide can be a liquid - I've still got two cylinders of the stuff sitting outside..... As for wood, it's not a compound or an element. It's a mixture of various things, some of which do melt and then turn to gas and burn if oxygen is present. If it isn't present in sufficient quantity, the gaseous stuff is just driven off and the wood becomes charcoal, which is virtually pure carbon. Carbon sublimes at about 3367 degrees C, and will boil at 4827 degrees (provided there's no oxygen around, of course!). Most things that are mixtures don't 'melt' as such, for the simple reason that the constituent parts have different melting points, or else under normal circumstances they will just burn, as jbean points out. Anyway, glass does melt, but as there are different mixes used to make different glasses, there isn't one fixed point for the lot.
http://www.madsci.org/posts/archives/sep2001/1000489806.Ph.r.html

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Afterthought: a whole class of substances that don't melt is the thermosetting plastics such as bakelite. They are made as powder, and set when heat is applied. If too much heat is applied, they eventually crumble or possibly burn. These are more like true compounds rather than being mixtures, like wood and potatoes are.

Glass does melt actually. Glass blowers practice their art by heating up the glass to the point where it melts and softens, only to harden again in its new shape while cooling.

CO2 also can be forced into a liquid state in a lab. Every substance in nature can be found as a solid, liquid or gas, and can take any of the three forms.

A graph for a substance that shows pressure on one axis and temperature on another and indicates the boundaries for the phases of solid, liquid and gases is called a phase diagram.
I have never seen a phase diagram with only two phases but then again, have never seen a proof that one cannot exist for some substance. I am less willing than Arpy to make such bold scientific claims without any strong evidence that counterexamples aren't lurking but he may be right.
Can anyone find a substance that has a phase diagram with only two phases, hence a substance which only exhibits two phases (or states) of matter? The question's assumption about glass is, of course, wrong.

I'm not so sure about glass boiling - partly because I've never heard of it happening, although that may be only because people don't usually let it get that hot or because separation of the constituents may occur. Arpy is right about elements existing in the three states (with the possible exception of carbon doing its subliming thing), but at least some other substances don't. As I said, thermosetting plastics won't melt but will degrade. Ice cream will certainly melt, but can it be found as a gas? Can you melt a potato? But the elements that make up the ice cream or potato certainly will (carbon possibly excepted) exist in the three forms.

In my personal opinion, everything, to an extent, will melt. My theory is that a burning substance will slightly become a liqiud and than that liquid would evaporate. The whole thing would not "melt, but some of it would for a split second. Melting is when a solid becomes liquid, scientists have never said anything about how much of a substanc must become liquid to consider melting.