I'm probably the forum's most defensive parker so I'll list some of my strategies, some that may be obvious and others you may not have thought about:
1. Runaway grocery carts (or heaven forbid, lumber carts at Home Depot - I saw a blazer's door get creamed just two weeks ago) - Scan the slope of the parking lot. Sometimes the safest space is the one closest to the building if the parking lot slopes away. If you can't park uphill, park right next to the cart return. People are more likely to put their baskets away properly who are parked closest to the cart return. Also, one side is protected from door dings.
2. Head to head parking - If there are bump stops, leave a good three feet between the opposite bump stop and your front bumper to allow for Corvette-like front overhang on any opposing car. With no bump stops, make sure your bumper is behind the yellow line.
3. Perpendicular parking - try to park next to cars that are shorter than the Supra. Parking between two 15-passenger vans may seem like a good idea since they have sliding doors, but it makes it difficult to back out and turn and you can't see whats coming.
4. Angle parking - real estate developers hate it because it takes more room to get their minimum required spaces but its one criteria I look for in choosing where I shop - seriously - theres a perfectly decent brand new grocery three blocks from me but I drive 7 miles away instead only because of the parking lot. Angled spaces are easier for the average one-handed cell phone talkin driver to negotiate without running into other cars. Also the steeper the angle, the less likely they are to ding your doors too.
5. Parallel parking - I look for the spaces on the ends of the rows so that not only is it easier for me, but exposes only one bumper to the neophytes who've never done it before. Actually, I rarely if ever park on the street anyway.
6. Parking garages - I will usually spring for the cost. Parking garages can have all sorts of layouts but a few things to look for: Watch where there are parking spaces along a tight radius turn. Never park in a space next to or along the inside of the radius. Sure as you do, some dumbass in a quad-cab, long bed truck trying to negotiate a garage built for subcompacts is gonna swipe your ass end. Best spaces are in outside corners where your car is well outside the turn radius and one side is protected from dings. Also, parking along an exposed face of the parking garage may defeat the purpose of having covered parking if the sun shines in that way. Also, pigeons often roost in parking garages so watch for poop stains on the concrete above and below and don't park in the pigeon's path.
7. Trees - It may seem like a good idea to park under a tree for shade, but remember that birds just hang their butts over the limb to so you might get bombed. Also, certain types of trees drip sap or have infestations of aphids that drip all over. Watch the ground under the trees for droppings. Birds may not be there now but mabe later. During the fall in Fort Worth, the grackles invade downtown each evening around 5:30pm. They flock by the millions and can ruin a paint job in a matter of seconds.
8. Know the parking situation before you go. Working downtown we have to deal with conventioners. I always keep up with what big conventions are to be in town each week. On a normal day, I park on the fourth level of the garage with mabe a half dozen other cars all spaced apart. If a big convention is scheduled, I get there an hour earlier and park on the lower level where I've scoped out four extra-wide spaces that are pretty safe, plus its a zip to get out at 5pm no matter the traffic.
9. Cadillac Eldorados and Olds Tornados - those doors are at least 12, mabe 15 feet long and and they're spring-loaded! Avoid them like the plague. Any two-door car with long doors can exhibit these characteristics.
10. Parking lot islands - Obviously parking next to the grassy islands in the middle of the parking lot can protect at least one side, mabe two from inconsiderates.
11. Lighting: Very important at night for general safety. I park right under a light post if I can.
12. Parking two-across - Don't do it. It may seem like a good idea but it draws attention to your car and provokes vandals. I've known friends who've had their cars keyed down both sides for taking up two spaces. Defeats the purpose.
13. Other cars - If you park next to an older car that looks like its well taken care of, then you can pretty much trust that the driver of that car isn't going to ding you. But if you park next to a beater, then you can pretty much bet he's going to ding you.
14. Wind - If the wind is blowing particularly strong, park facing into the wind such that cars on either side are parked facing into the wind. If the wind is coming from behind it can catch a neighbors door (or yours) and catapult it into the car next over. We learned this the hard way at a Supra event when we lined up cars the wrong way and myself and three others got got in the space of two seconds just not paying attention.
15. Fat people - No offense, but if I see that a heavy person has just gotten out of a car, I will not park next to it. Just a fact of their existence they have to swing the door as wide as it will go to get back in.
Just a anecdote to show just how anal I am about parking - About a month ago, one of my coworkers was complaining of chest pains and I asked if he needed an ambulance. He said no but perhaps he'd better not drive himself home. I offered to drive him. On the way, his pain got worse and he said "take me to the hospital." We get to the hospital, Victor is clutching his chest and hyperventilating and there's no spaces open at all but then someone pulls out right up front leaving the tinyest space with one old beater car parked over the line and I look over at my dying friend and say "Dammit, I can't park THERE! Given the look on Victor's face, I did anyway, checked him in to emergency and then ran back out to move my redpra. Thankfully it was fine and so was Victor, just an anxiety attack they said.