Stability and resonance structures
Stability is a funny word. It gets tossed around all the time, but a molecule's stability really depends on the context you are considering it in. For example, benzene is totally unreactive towards electrophilic addition of $\ce{Br2}$ like most alkenes, but $\Delta_\mathrm{f}H^\circ(\text{benzene}) = 49.0\ \mathrm{kJ/mol}$, while $\Delta_\mathrm{f}H^\circ(\text{cyclohexane}) = -37.8\ \mathrm{kJ/mol}$.

So when we talk about resonance and stability, what are we really talking about? What this really refers to the stabilization energy associated with conjugated systems. For every p orbital that is added to $\pi$-system, it mixes in phase to create a new molecular orbital that is lower in energy than the two starting orbitals, or mixes out of phase to create an orbital that is higher in energy than the two starting orbitals, and in some instances doesn't mix at all. This is illustrated here:



You can't directly compare the relative energies of the molecular orbitals of two unlike molecules simply based on their number of resonance structures, though. Different atoms and substituents will cause deviations and make comparison meaningless, so it is really only useful to compare homologous compounds, like butane, but-1-ene, and buta-1,3-diene.