The people I know who back in do it for masculine posturing, so you can make a “quick getaway”. They do it everywhere, not just where you could see the advantage.
I am a retired (American) soldier and work on a (Saudi) airbase.
I have noted most of us retired soldier/airmen types “combat park,” in that we park nose-out for a quick getaway.
Re Otto’s question about some places barring back-in parking.
I’ve also seen that at restricted parking facilities where the sticker identifying the car as OK to park there is rear-mounted, and prohibiting back-in parking allows security people to easily see the sticker as they cruise around the lot.
Diagonal parking is marginally better than parallel parking on a busy street. Otherwise it is clearly a sign that Satan is active in the world.
I’m not sure where this idea comes from. I do the same whether or not I will be observed. Considering the abuse I encountered from guys for backing in when I first started driving, it certainly never seemed like a “guy” thing to me.
Related to Zsofia’s answer, it’s because of time for me. Backing up takes a hair longer so I generally decide that it’s better for me to get it out of the way in the morning (and be a tad later for work) and be able to leave for home faster. This is important when the exit out of our garage is onto a very major street and even 2 seconds can mean that I might be stuck behind 5 cars (all of whom are generally too scared to pull out into an empty right lane when the lane to the left is full), which means I’ll be stuck at another light, which means I’ll be stuck by another light, and another light. (You make one light you make them all. You miss one, you get stuck by them all.) Backing in at work can save me 2 or 3 minutes of traffic.
At the grocery store or whatever, I’ll usually only back into a spot to get a spot closer to the door. These spots are usually angled though.
Some parking brakes apply to the front wheels. Most cars are front wheel drive, and will be in park (automatic) or in gear (manual). It doesn’t really make sense for that to be the reason.
I’m very good at parking, simply because I am a forklift driver. If I wasn’t good at it, there’d be something wrong. Ironically, the problem this gives me is with on-street parallel parking. I can slot my car into a space with only a few inches front and back - but I don’t trust the other two drivers not to hit my car when they leave. So, many times I have to ignore a space I could use, and spend another five minutes circling around.
With 90 degree angle carpark parking, I just drive straight in. The only exception is in my carpark at work. If I’m going out for lunch, I’ll drive straight in, but when I come back from lunch I’ll reverse in because at the end of my shift there are about fifty cars all leaving at once, and there is a traffic jam up the main carriageway. If I nose out, I can be aggressive and push in. If I back out, the other drivers have left me no room to swing back, and I’ll be the last to leave, ten minues later.
For most situations, I’d recommend just driving in. When I don’t have my car, a friend drives me to work. She hates reversing in or out. So the deal is I do all the reversing, and I get to use her car at lunchtime. She drives in at the start of shift, and I back it out at lunch. When I come back with my burgers, I back it in for her. In the evening, she drives out. I am a parking whore! 
From my own personal experience I have noticed that the cars that back into the parking space are far more likely to take up more than their own space. I often wonder how they can fail to see that they are parked way over the line once they get out. Maybe they are just to lazy to correct it.
I have to admit that I rather like reversing into parking spaces myself; my drive slopes downward, then joins at right angles with a piece of shared-access land turning to the right, then joins the road at right angles to the left. in order to not drive over next door’s garden, I have no choice but to reverse all the way through the zigzag bit - I could do it with my eyes closed now (not that I will, you understand.)
Otto: Some state issue only one licence plate, and those that issue two issue only one registration sticker. Cars that are parked head in have the plate/registation exposed for insepction by authorities, while those backed in do not.
Well, Texas doesn’t have a sticker on EITHER plate anymore. It goes on the windshield. And backing into a space isn’t illegal here, not in Houston anyway.
Looks like most of the reasons have been covered , so how about this one.
I’ve got an old '65 Ford pickup that I’ve restored. Problem is that I don’t take it for any long drives. Just a lot of short errands and such. As a result every now and then the battery is weak. So, I back that old truck into a spot with a bit of slope and pop the clutch on the roll if necessary. Then I take it for a spin to charge it back up.
When I take the car to go grocery shopping, I usually back into a spot so the trunk is near the store sidewalk and awning. This way I can just load up into the trunk and never have to walk across the parking lot with a buggy.
Works great in the rain. 
Also have a “get away” mentality as well.
My dad started backing into his driveway because he was a volunteer firefighter, and it’s quicker to drive out, and since he would be in a hurry if there was a fire, he might be paying less attention. If you are already forward, you are more likely to see a car coming. That just transferred over into backing into a spot. Though it is easier to back in, for reasons stated above. Rarely from backing in do you have to go back out and then in again to align properly, wheras gonig in frontways this is common if there is little space, or you start to pull in to close to the other parked cars.
One more (admittedly very minor) reason for backing: if your battery dies, you can bring another car close to the hood for a jump even if your parking space is surrounded by other cars.
Here in Tokyo there are a some small parking lots that forbid backward parking. The reason seems to be that the adjacent business or home complained about car exhaust directed into their property.
IIRC its because if you back out of a spot, in the event of a collision an oncoming car will hit you on the back right corner, a minimal threat to the most comon occupant (the driver). When you pull out forward it puts you closer to the theoretical point of impact in any accident that would occur. When backing out a driver coming from the drivers side has a little more time to react because he is usually more to the left side of the “lane” in the lot.
And then there are the people who purposely park diagonally across two spots, to protect their car from door-dings.
I always wished I knew some bikers I could call to park all around Diagonal Man …
IIRC its because if you back out of a spot, in the event of a collision an oncoming car will hit you on the back right corner, a minimal threat to the most comon occupant (the driver). When you pull out forward it puts you closer to the theoretical point of impact in any accident that would occur. When backing out a driver coming from the drivers side has a little more time to react because he is usually more to the left side of the “lane” in the lot.
The gangsta street racer crowd likes it because its easier to pop the hood and show off your new chrome engine detail kit.
I heard somewhere AFV cews taught to park back to back or back up against something to help cover their lighter rear armor in the event they have to mount up under fire… probably also has something to do with the fact that you will have to stop and make the transition to moving forward, whereas a stright pullout will not require it. Only saves a few seconds but a few seconds is an eternity in a firefight.
Just go give a tire a kick. They will be all freaked out when their uberalarm pages them in the store or the alarm light is blinking that the alarm was set off.
Oh, this thread is about vehicle parking.
Thoughts elsewhere.
Me bad.
Carry on.