I am the paranoid king of parking.
I find the largest, furthest parking spot. I especially like the spots next to handicap parking because (a) the handicap slots are HUGE and amost always empty and (b) You can gain an inch or two by crowding the yellow lines that delimit the handicap slot. If you are adventurous you can sometimes get away with crowding most of the yellow line, though past a point you risk a ticket, and there is the off chance that some deserving soul with a gigantic vehicle will take up the whole slot and expose your baby to damage.
Study the parking lot. There might be a slightly wider spot somewhere where the geometry didn't quite work out.
Note the wind direction. I have seen clueless people open doors in a strong wind and have the door fly out of their hands to ding the car next to them.
Don't park in the middle of anything. I got hit by some idiot in a landscaping truck who backed halfway across the parking lot to ding the car.
Don't be a jerk and take up two spaces, that is inviting a keying. In fact, don't be annoying in any way if you can avoid it.
Park where you can monitor the car. If you see some idiot approaching, go out and move your car.
If somebody has parked next to you despite your best efforts, double check for dings before driving away. If they got you, you can deal with it if you are aggressive. Don't be a jerk, chances are they didn't mean to ding you, they're just clueless dolts.
Use any available cover. Light poles, trees, trash, derelict vehicles. Dumpsters are great, they usually take up a space and a half and you can use that safe space to your advantage. Just make sure the truck isn't coming to pick up the dumpster, though! I have even toyed with the idea of bringing my own "debris" to place in the spot next to me to discourage door-dingers from parking adjacent. Let us know if you try that and it works!
The key is to put the car far enough away that it is out of the traffic flow, and not in a place that people will want to walk direct to and from their vehicles. Traffic means some numbnuts might drive into you, and foot traffic means subhumans might randomly vandalize your car on the way to buy their hooch. Don't give anyone a reason to walk past your car.
Pay attention to the slope of the parking lot (especially in a supermarket lot). Never park downhill from any occupied spots (because Gooberhead is sure to lose control of his shopping cart and blam!). In shopping center lots there is a corral for the carts-- Often a good thing to park next to, just be sure you are uphill from anything else. Clueless dolts will launch their carts from half a mile away in the vague direction of the corral, which is a problem because the carts are drawn magically towards nice cars. But an uphill slope means the idiot will have to manually put the cart in there, and her probably won't hit your car.
Find another nice car to park next to. If some guy is obviously trying to protect his car, do him a favor and guard the other side. I find that people who care about their cars will generally be careful of another nice car next to them. Just don't park 3 inches away without their permission.
Avoid child care parking lots like the plague. Ditto for any place that teenagers park. Never ever park at the closest spot to anything worth going to, even if the slots are huge.
Bottom line, be paranoid. The world is full of Door Ding Idiots and they are reproducing. They really want to ding your car, but you are smarter than them.