The core issue with karate is that it is loaded with formal or ritualistic representations of fighting. Karate kicks, punches and blocks are all hopelessly unusable when fighting a boxer for example, who is trained to defend their head and hit their opponents head hard and fast. By contrast, few, if any, karate stances are explicitly defending the head from being hit. The more extreme examples include holding the fist at the hip - a truly useless place for a fist to be during a fight.
Primary head defense in most karate stances is distance.
Distance did not help. At best, a punch or kick or two were thrown, and then the grappler was able to close the distance, and then anyone who didn't study grappling (or at least wrestling) was at a massive disadvantage, and the fight quickly ended in the grappler's favor.
In general, any martial school that focuses not on competition, can be good (the set of techniques are not really that different, they're all ways for one human to break another human - physics and biology dictates what falls out as efficient).
Judo can be efficient self-defence in a club that tries to focus on the early martial arts curriculum (but generally fails miserably at teaching strikes and kicks). One benefit of judo is that it (should) teach good ukemi (how to fall) - I usually say that knowing ukemi is knowing how to block the ground. A large number of real-world injuries come from hitting your head on the ground or on the curb, so being able to get up (and run away) from being thrown to the ground is a good start. Not to mention some grappling can go a long way if you find yourself in an intimate situation that you only too late realize is turning into an attack. This also holds for brazilian ju-jutsu (which despite it's name is more like early judo practice, than traditional ju-jutsu) -- but I've yet to see many bjj dojos that have a reasonable focus on throws and efficient ukemi (which makes sense, if you focus on a sport that does mostly take-downs and not throws).
That said, most big martial arts can be great for self-defence, if the instructors have an interest and are competent in self-defence. But practising real-life self-defence isn't really pleasant - so doesn't go well with typical "martial arts for exercise" type programs.
I studied Tang Soo Do for many years, and the really useful self defense techniques were not taught until I got my black belt, and we started learning techniques from different martial arts.
This teaching was deferred primarily because the useful techniques can be extremely dangerous to practice (strikes to the throat being a good example, and grappling techniques where you maximize leverage with the intention of breaking bones).
MMA can mean many things; I usually read it as the modern circus that is UFC etc - a sport.
Krav Maga is self defence (or self offence, it's pretty violent; it's for situations where you'd be justified in using lethal force, not for "scuffles"). It's simple, and has a curriculum that's built around survival; you'll typically see something that looks a lot like Krav Maga in any martial arts self defence class (if it's any good). And you can typically find "krav Maga" techniques in any martial art. For example one of the first techniques thought in taekwondo is the straight front kick, the first movement of the kick is lifting the knee - so you start practicing a knee to the groin as a white belt. But sadly you could become a fifth Dan in taekwondo and not even realize that, because of the sorry state of self defence in a lot of taekwondo dojangs.
Taekwondo, I think, long ago parted ways with any intention of being an art of self defense, if that intention was ever there to begin with.
Two typical examples are: tomoenage that in its original jujitsu form was a kick to the groin, but in judo is a foot to the hip; first you can't go and kick your practice partners full force to the groin (without them wearing protection - hence you can't really practice the actual technique) , and second if you kick someone in the groin they'll roll up, and the throw becomes ineffective (although you could argue that a good kick or two to the groin is usually quite enough. But only if you actually hit. A good landing on the head is also quite effective). And ipponseionage which in a jujitsu variant involves crossing the arms in an elbow lock, hoping to break the lower arm in the throw - but also becomes a slower and less efficient technique.
So the safe set of judo techniques makes for very good sparring practice. But it won't prepare you for a thumb in the eye or a bite to the face. Or being stomped on the head while grappling.
Basically, if you're not actually fighting, you don't know how to fight. It would be like learning how to program, except you've never actually written a program before.
One of the unfortunate lessons I learned early on in real life, is that "self defense" systems which only cover one-on-one fighting (eg the Tae Kwon Do schools I've seen) are close to useless in real life. eg in a bar fight, or a group of drunks decides to pick on you when you walk past. I'd studied Tae Kwon Do for about fours years before discovering this (the hard way doh!). :/
With Ninjutsu and Arnis (at least some schools), training for combat against multiple opponents is a core part of it. So, less likely to suck in real world situations.
If you're in Australia, this group seems legit (I used to train with them years ago): http://www.tesoma.com
BJJ is probably the most useful for self-defense (personal opinion), but it's also the most complicated to learn. It covers ground fighting better than wrestling or judo, which is where many situations will eventually end up. If I had to pick one, excluding MMA (which is basically a combination of everything listed), I would make it this.
Wrestling and judo for takedowns and takedown defense. Judo is more complicated and difficult to learn than wrestling (imo), but, depending on your age and physique, wrestling may be of limited use to you (a 50+ year old will likely have trouble applying many of the wrestling takedowns). A lot of what you'd need from these two would be covered in a BJJ school anyway, just with less time and focus spent on those areas.
Boxing and kickboxing to learn how to defend yourself from strikes. Again, depending on age and phyisque they may otherwise be of limited use, since an older or smaller person is unlikely to be punching with knockout power, and would run a higher risk of breaking bones in their hands when striking.
An MMA school would tend to cover all of that, but they may be more focused on competition than self-defense, which will affect what they teach you and how you train. Same problem with BJJ schools - a lot are more concerned with tournaments than self-defense, which can change the focus of your practice considerably.
But if what one wants to learn is primarily "self defence", then one has to, unsurprisingly, practice self defence. Practice the type of situations you want to defend yourself from. I could probably link to videos all day, but eg: this one with Phil Thompson explains some of the basics (despite the cheezy intro):
"Protect Self Defence on TV3's Pacific Beat Street" https://www.youtube.com/watch?v=LLkKE-gSuj0
Some more snippets with Thompson:
"Self-Defence Seminar with Phil Thompson - The Passive Stance" https://www.youtube.com/watch?v=S9cU6yGSgB8
"Self-Defence Seminar with Phil Thompson - Wrist Grabs" https://www.youtube.com/watch?v=KlI3rzsml_g
There's also something to be learned from military martial arts, like (this is more typical Martial Arts wanking, so to speak, but I really love this guy):
"Systema Demonstartion on Korean Special Forces" https://www.youtube.com/watch?v=SfHfua9ku4s
Note, don't put too much emphasis on the "Systema"-bit, DK Yoo probably holds high level dan grades in more martial arts styles than I even know about. That said, Systema is a very interesting style - developed by and for the Russian/Soviet special forces with inspiration from traditional Russian wrestling and judo -- it's a surprisingly soft style for a modern military martial art. Like man other styles, if you can find a good instructor/dojo I'm sure it can be a perfectly fine approach to self defence. But as Thompson says above, it's not the physical techniques that are the hard part.
The reason I call out Krav Maga (developed from practical self defence in the Warsaw ghettoes, and evolved by the Isreali military and special forces) is that it is modern (as in new), it has a pretty reasonable and well-functioning system of grading instructors - so if something "really is" Krav Maga, it's a bit easier to know a little about the quality of the training - unlike, say "karate" or "jujutsu" - or "taekwondo" (which encompass everything from the funny stuff that is in the olympics to more traditional stuff that is closer to the founder's original vision [ed: note that the second two videos with Thompson is from a taekwondo seminar, so there are obviously still places where you can practice taewkondo and actually learn something useful]) - and the general civilian training (to the best of my knowledge) has a strong focus on self-defence - practising actually useful stuff like verbal assault, multiple attackers, situation awareness and so on.
It very much is a system for self defence, while most other things one could practice ends up being "martial arts with self defence added on". Personally I prefer that, I don't really enjoy practising just self defence - not to mention the fact that I'm not entirely convinced there are enough situations that are dangerous enough that I really need to defend myself violently, and yet not so dangerous that I won't simply be stabbed to death or shot -- that's its really worth the effort to practice all that much with the aim of self defence.
But practising any kind of physical confrontation for fun will boost confidence, and give one a better idea of when a situation is dangerous, and how it might be dangerous.