The physical properties of substances having molecular structures varies with the type of intermolecular attractions: hydrogen bonding or van der Waals forces.
Molecules are made of fixed numbers of atoms joined together by covalent bonds, and can range from the very small (even down to single atoms, as in the noble gases) to the very large (as in polymers, proteins or even DNA). The covalent bonds holding the molecules together are very strong, but these are largely irrelevant to the physical properties of the substance. Physical properties are governed by the intermolecular forces - forces attracting one molecule to its neighbors - van der Waals attractions or hydrogen bonds.
Melting and boiling points
Molecular substances tend to be gases, liquids or low melting point solids, because the intermolecular forces of attraction are comparatively weak. You don't have to break any covalent bonds in order to melt or boil a molecular substance. The size of the melting or boiling point will depend on the strength of the intermolecular forces. The presence of hydrogen bonding will lift the melting and boiling points. The larger the molecule the more van der Waals attractions are possible - and those will also need more energy to break.
Solubility in water
Most molecular substances are insoluble (or only very sparingly soluble) in water. Those which do dissolve often react with the water, or else are capable of forming hydrogen bonds with the water.
Why doesn't methane dissolve in water?
The methane, CH4, itself is not the problem. Methane is a gas, and so its molecules are already separate - the water doesn't need to pull them apart from one another. The problem is the hydrogen bonds between the water molecules. If methane were to dissolve, it would have to force its way between water molecules and so break hydrogen bonds. That costs a reasonable amount of energy.
The only attractions possible between methane and water molecules are the much weaker van der Waals forces - and not much energy is released when these are set up. It simply isn't energetically profitable for the methane and water to mix.
Why does ammonia dissolve in water?
Ammonia has the ability to form hydrogen bonds. When the hydrogen bonds between water molecules are broken, they can be replaced by equivalent bonds between water and ammonia molecules. Some of the ammonia also reacts with the water to produce ammonium ions and hydroxide ions.
\[ NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^- \nonumber \]
The reversible arrows show that the reaction doesn't go to completion. At any one time only about 1% of the ammonia has actually reacted to form ammonium ions. The solubility of ammonia is mainly due to the hydrogen bonding and not the reaction. Other common substances which are freely soluble in water because they can hydrogen bond with water molecules include ethanol (alcohol) and sucrose (sugar).
Solubility in organic solvents
Molecular substances are often soluble in organic solvents - which are themselves molecular. Both the solute (the substance which is dissolving) and the solvent are likely to have molecules attracted to each other by van der Waals forces. Although these attractions will be disrupted when they mix, they are replaced by similar ones between the two different sorts of molecules.
Molecular substances will not conduct electricity. Even in cases where electrons may be delocalized within a particular molecule, there isn't sufficient contact between the molecules to allow the electrons to move through the whole solid or liquid.