With that said, stability shoes work well for overpronators. Stability shoes are usually built on a semi-curved last to accommodate a bit of an arch. In addition, the last is straight to accommodate flatter arches. Motion control shoes are for extreme overpronators. Neutral shoes have a uniform color and uniform density throughout the midsole.
Neutral shoes are for neutral runners and udnerpronators.
Underpronators and supinators need shoes that encourage pronation. Don't let this confuse you. All shoes have a cushioning system. Okay, you should be armed with enough knowledge to know what kind of shoe you're looking for. For those interested in more details, I will now throw in some further bits of information for your studying enjoyment.