[kfa]

Why is it that certain substances, (example: solid carbon dioxide) can undergo sublimation and turn into gas without undergoing liquid form when heated?

What is the general characteristics that enable certain substances to undergo sublimation?

Is it possible to have a substance that can undergo sublimation and melting process when heated?

[Yggdrasil]

Whether a solid melts or sublimes depends on the pressure of the system relative to the pressure of the substance's triple point.  Basically, below a certain pressure, a liquid cannot exist because the interactions between molecules are not strong enough to maintain a liquid state.  For carbon dioxide that pressure happens to be above atmospheric pressure (since the interaction between carbon dioxide molecules is very weak).  For water, this pressure is well below atmospheric pressure.  But, if you put ice in a chamber with very low pressure (< 600 Pa), you can get ice to sublime.

For more info see wikipedia or look up phase diagrams/triple point in your chemistry textbook:
http://en.wikipedia.org/wiki/Triple_point