Why do substances like camphor experience a phase transition from solid directly to gas when they are heated? Why don't such materials behave like water, and experience a liquid phase?
Materials will sublime (go from solid directly to gas) or deposit (go directly from gas to solid) if the pressure is correct, or they will go through the "normal" three phase transition (solid to liquid to gas, or reverse) at other pressures. You can tell based on the phase diagram, which is for $CO_2$:
Carbon Dioxide, like Camphor, sublimes at normal atmospheric pressure. In the above diagram, you can see that at 1 bar (which is close to atmospheric pressure), the solid and vapor regions border each other, but at higher pressures, such as at 10 bar, it will go from solid to liquid, then to gas, as temperature rises. I don't have a phase diagram for Camphor, but I see no reason why it would act different; the pressures required may be different, but the overall idea is the same.
Water can also sublime or deposit, but the pressures required for this are much lower than atmospheric pressure; see a phase diagram of water for details.
Additionally notice that molecules which sublime at atmospheric pressures like $CO_2$ and Camphor are non-polar or only slightly polar. This means that there will be far less inter-molecular attraction compared to a very polar molecule like water, which can engage in hydrogen-bonding; due to the low attraction between non-polar molecules, they can "fly off" a solid directly into the gas phase, since there won't be any attraction keeping them condensed in a liquid.