I'm confused whether it's the intermolecular forces, or the bonds that are being broken when a substance changes state? Does this differ among different types of compounds (eg. covalent, ionic, covalent network solid? What is actually happening when they change state?
It could be either chemical bonds or weaker intermolecular forces that change during a change of state. Water is held together by hydrogen bonds and make its boiling point higher than for analogous compounds.
Sulfur changes both ways with temperature:
Sulfur forms polyatomic molecules with different chemical formulas, the best-known allotrope being octasulfur, cyclo-S8... At 95.2 °C (203.4 °F), below its melting temperature, cyclo-octasulfur changes from α-octasulfur to the β-polymorph. The structure of the S8 ring is virtually unchanged by this phase change, which affects the intermolecular interactions. Between its melting and boiling temperatures, octasulfur changes its allotrope again, turning from β-octasulfur to γ-sulfur, again accompanied by a lower density but increased viscosity due to the formation of polymers. At higher temperatures, the viscosity decreases as depolymerization occurs. Source
Metallic bonds are delocalized, so in melting, there is no real change in bonding (though on boiling, a metallic vapor is quite different).
One could say, though, that this is simply a matter of definition: chemical bonds act over shorter distances, and intermolecular forces over longer, but they are not intrinsically different, the polar or hydrogen bond being an example of one that bridges these realms.
In reality if a substance is in liquid phase , then not all intermolecular bonds are broken between molecules but some of them and this results in the creation of groups of molecules.In gases all intermolecular bonds are broken between molecules.
The intramolecular bonds are not broken during a phase transition and that is why I posted my own answer instead of comment on DrMoisphe's answer.