Most auto mechanics that love working around cars, can think back to their early years and remember when the day's biggest concern was if their bike had the right amount of tire pressure.
You might have come a long way since then, but the basics are still the same. When your tires are properly inflated, you're more than likely to experience the comfort, performance and durability that most cars were meant to have.
Because of under-inflation, the thread life of a tire can lose up to 25% of its normal life span. If your tire is just 6 psi under the normal limit, this could actually weaken the tire's internal structure, and eventually lead to tire failure.
There would also be a noticeable difference in steering and cornering capabilities.
An over-inflated tire can be present road problems as well. Over-inflated tires tend to be stiff and unyielding. There is also the challenge of isolating road irregularities, and there is a tendency for more noise to make its way to the car's interior.
On a positive note, higher inflation pressures can reduce rolling resistance, and will typically provide a slight improvement in steering and cornering. Driver's who use street tires for autocross, track events, and road races; usually use higher than normal inflation pressures.
Tire deflection will remain as originally designed when the correct tire inflation is properly maintained. Heat buildup will also be managed more efficiently, and your car's ability to resist rolling will be enhanced.
If you're into "wrenching", and working on cars is the next best thing to breathing oxygen; this could be the start of something great.