I have never read a Batman comic. Everything I know about the Joker I know from the Dark Knight, TVtropes, some parts of wikipedia, and popular culture. I wish to be educated on what makes him so dangerous in the comics. Which issues should I read in order to eternally fear him?
Couple thoughts about this:
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If you aren’t familiar with sociopaths in general, you could start there. Basically, the Joker is absolutely and completely without morals or a conscience, which makes anyone dangerous. I would recommend reading www.crimelibrary.com and Frank Miller’s Dark Knight series. In a nutshell, his insanity makes him absolutely and completely unpredictable.
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The Joker is basically a deux ex machina. He has been characterized over the years as being able to accomplish just about anything he wants to. In some sense, he is omnipotent and infallible as needed in the plot, in much the same way as Luthor. A good example of this aspect of the Joker is the movie the Dark Knight, where it seems like the Joker knows exactly where Batman will be and in some cases, appears to be in two places at the same time.
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As Batman’s archenemy, he’s essentially as powerful as Batman, which is pretty tough in and of itself. Luthor, for example, gets a lot of props simply because he’s able to put up a reasonable offense against Superman, as the Joker does against Batman, or the Red Skull against Captain America.
He’s extremely well funded, he’s got no conscious, and he’s brilliant. Maybe smarter than Bruce Wayne, who’s alluded to be a high level genius in more than one comic.
What could be more danger than a well funded, brilliant sociopath? A well funded, brilliant sociopath with a vendetta – and that’s the Joker.
And the Joker is not only amoral but whimsical. Other superbaddies will kill for money or power; the Joker will kill for fun. He will even kill when not killing would seem to be more in his interest.
Because he kills onstage.
basically for the same reasons batman is so dangerous. batman for not having any superpowers really kicks the tar out of some super-baddies. joker is essentially what batman does, but for the other team… plus he kills.
Batman’s Jungian shadow, then?
Kind of. Look at this exchange between them in the Dark Knight. Batman does not let the Joker fall to his death, and the Joker just finds that hilarious.
He’s also GenreSavy and can often break the fourth wall, due to his craziness. A bad guy that knows he’s in a comic, and knows the rules of that comic? Even without the sociopathy, that’s a dangerous villain.
If one of the characteristics of the Shadow is a much, much better sense of humor.
What everyone else said, but also:
The Joker can create followers just by being near them long enough–first, he breaks their spirit, then, he drives them crazy, then, he makes them loyal to him. Then, of course, he sacrifices them uncaringly. And all through sheer force of will.
As such, he is near-impossible to contain. Any prison he is in will soon become his kingdom given enough time. He’s got loads of contacts, both inside and out. And he’s so crazy that even in the most remote and isolated cell, the guards still let their guard down around him. And, of course, Batman won’t kill him…but he’s the only one with enough willpower to defeat him. Thus, the constant Joker prison breaks.
The Killing Joke by Alan Moore made two things pretty clear: He’s crazier than you suspect. And while Batman is stronger and more skilled, the Joker is actually a lot faster.
He’s not just insane; he is, in some sense, insanity itself. His madness is contagious. Consider, for instance, Harley Quinn, who started out as a perfectly sane, normal, and law-abiding psychiatrist (though, of course, with a name that doomed her), who attempted to treat the Joker during one of his stints in jail. The result? She’s now a Queen of Crime in her own right, and madly in love with the Joker.
Hell, yeah! I’m ready to kill for him, and I know he’s fictional! 
The Joker is the very definition of ‘Other directed,’ his motives can’t be understood, so he can’t be reasoned with or bribed. Many villians persure money or power or revenge, a few, like Freddy or Jason don’t appear to have a motive, but The Joker raises unfathomability to an art form.
He’s a genius, he is incredibly tough, he is completely ruthless, and he just doesn’t give a damn.
As one well known person says, “Some men just want to watch the world burn”.
He is exceptionally gifted in technology, especially chemistry. In particular, psychoactives & toxins.
This.
Other Bat villains have superpowers, more resources, more henchmen etc. But they can be predicted and understood. The Joker does things for no sane reason.
In one issue, he pushes a henchman in front of a speeding car just for asking ‘Where ya goin boss?’
Everyone else is answering the why question, so I will try to take on the what question.
Without question read The Killing Joke
If you can track down this collection it is well worth the price of admission also, and contains my personal favorite Joker story “The Laughing Fish”. More than that, it shows you a lot of variations on what the joker can be and has been over the years. It’s a great primer.
I also liked this. But I really liked Ed Brubaker
And rounding things out would beArkham Assylum which is…different. But good.
Read those, then watch some Batman: The Animated Series joker episodes (Mark Hamil was the definitive Joker) and then you should be hooked.
I actually wouldn’t recommend that to someone who’s not already familiar with the characters involved. I have a friend who read it without the background, and I spent a lot of time explaining stuff to her, and she still found it more confusing than it was worth.