The "real world" as you might surmise from the "world" part is a big place, and things are quite different in one part of the world from another. There are many different situations which might call for self defense, some of which only affect some people and others which only affect different people. So for the question to really garner a useful answer you have to specify which "real world" situation you are concerned with in particular, and what type of person you are.
For example, I know in Vancouver a number of women who have been mugged, yet have never been hurt as they merely gave up their purse and whatever contents it had. That's getting out of the situation safely, and they didn't need any self defense training to be able to use good sense.
Now in other parts of the world, I understand muggings can be fatal. Simply giving up your posessions will not necessarily keep you safe. So where do you live, how do muggings play out where you live, in your neighbourhood?
In some parts of the world you have to worry about car-jackings. That's not a concern where I live, so the extent of my knowledge on that is that apparently in Johannesburg people have flame throwers built into their cars to defend against them! Clearly if you live in Johannesburg, technology is of far greater value to you than any martial art training could be.
Another situation, while living in a more rural area I had a serious concern about dogs near the suite I was renting. One of them was a Rottweiler, and while it was always on a chain, it would charge at me as I walked past on the road with so much force that when it came to the end of the chain it would swing around. Clearly if the chain broke, or the owners neglected to tie the dog up, I was screwed. I carried an umbrella with me, even on days with clear skies, as I figured it might work as a shield for me. Most importantly though, I moved away as quick as possible. No martial art I'm aware of teaches you how to fend off an attack by a Rottweiler. With trees nearby, assuming I could sprint to them fast enough, callisthenics training in the style of BarStarzz (check them out on YouTube, they're quite inspirational) might have allowed me to get into a high branch quick enough, but again, that's not a skill any martial art would give me.
Speaking of running and getting into trees, many martial arts will pay lip service to running, but how many of them even have you do sprints as a warm up, let alone play an important part of the training. You'll have to do Parkour/Free-Running for that. Many martial artists seem far more interested in talking about the importance of running while instead training to stand their ground and fight.
Are there any local combat sports that are popular? Wrestling is quite common here, so you'd better know how to deal with it. For those who would like to bring up a point that wrestling has rules, I'd like to introduce you to the term "oil check". For those unfamiliar, it involves jamming a finger into the opponents rectum to have better control of their hips. It's quite illegal in competition, but it still has a name for it. Wrestlers fight dirty, they're also very tough and headstrong.
Has MMA taken off locally? Stephan Kesting in one of his seminars brought up an rather depressing anecdote about a fight between two hobos in which one of them went for a guillotine and pulled guard on the other. Make sure you know how to fight better than someone who has just learned from watching UFC through the window of a bar. I know from experience (being the person doing it) that just knowing the strategy of taking the fight to the ground and going for a choke is enough to defeat a number of martial artists with years of training. That's also why so many TMAists will try to list a bunch of reasons why you don't want to go to the ground in a "real fight", they're unwilling to admit their style has a huge gaping hole that needs to be filled by BJJ.
What's the gun situation like? Are they commonly used in crimes where you are? If so, don't just trust any MA instructor that claims to teach gun disarms. There's a ton of useless stuff out there in the realm of gun disarms. Most of the stuff that is taught will get you shot - whether that gets you killed is a question of luck.
Is there wildlife where you are? Bears perhaps? That fish commercial from 10 years aside, no style will teach you to beat a bear. Bears also run incredibly fast, and contrary to popular belief, Grizzlies can climb trees. Not only black bears. Mace can be effective, primarily to dull their sense of smell so they can't track you as you make an expeditious retreat, but what you really want is a treeing dog, so called because it will chase bears into a tree rather than running as fast as it can to bring the bear right back to you.
If you're a woman concerned about being raped, hands down BJJ is the best style to practice. No other style comes even close in specificity of skills taught for dealing with a rape situation. Anyone who tries to tell you otherwise is trying to cover for their own style's inadequacy in this department.
As a bouncer I've found wrestling to be by far the most useful. I clinch and talk to the guy until he settles down. It's clear I'm trying to de-escalate, so his friends actually side with me in order to keep anyone from getting hurt. They appreciate it. One guy I had to deal with, whom I handled without throwing a single strike, taking him to the ground or causing any sort of injury actually had my back in a different fight 5 months later, which was quite welcome given we were understaffed. Does the style that teaches real world self defense teach you to consider the aftermath of the fight and use restraint whenever possible, or does it try to work you up into a blind rage where you think every altercation has to be dealt with extreme, psychopathic violence? Other bouncers who rely on boxing instead of wrestling find themselves getting dogpiled once they punch someone. In reality, it's striking that has you dealing with the guy's friends trying to kick you in. So the striking exponent who says you don't want to grapple because of dealing with some guy's friends believes so because of a self-fulfilling prophesy. His approach leads him to having to deal with multiple opponents simultaneously. My approach has my opponent's friends supporting me to de-escalate the situation.
Now if there were a culture of saving face, where someone couldn't maintain their honour, or somesuch, by walking away from a fight, then my approach might no longer be reliable. But what I have done is tailor my approach specifically to my environment to give me the best chances taking everything into account. Know your area. Know the people in the area. Know how they'll react in the short term and the long term based the actions you'll consider taking.
Based on that analysis of your particular situation, determine which styles best suit your situation, and as others have said, which instructor teaches with the best eye to dealing with your situation. And it has to be your situation, an instructor with a fondness for drinking who gets his experience from barfights isn't that great of a source of information for you if you're a sensible person who doesn't drink to excess and get into fights at bars.