
In this landmark story, Jason Todd, the second Robin, had his fate placed in the hands of the fans of the comic, who narrowly but decisively voted to have the Boy Wonder killed. Who better than the Joker to do it? And we see the clown at his most viciously murderous, as he takes a crowbar and, smiling the whole time, proceeds to beat Jason to a bloody, messy pulp. This of course sends Batman into a vengeful rage, leading to a confrontation that leaves both smarting.
A personal favorite. Tim Drake, the third Robin, is still fairly new in his crimefighting role when circumstances dictate a harrowing situation: the Joker breaks out of Arkham and Batman is out of town. When he confronts the Joker for the first time, the look of shock and surprise on Joker's faces is priceless. "YOU..." he says. "I KILLED YOU..." When Robin manages to put him away without his mentor's help, the Joker swears it's personal now.
Batman's caught Joker after a rough night, in which the clown has crippled Barbara Gordon and nearly driven Jim Gordon insane. After trying to reach out to the Joker and get him to help end their long feud, the Joker declines and tells Batman a joke. As he starts to laugh helplessly, Batman's stoic exterior fades, and he joins the Joker in his laughter. This is the one time I've ever seen these two laugh together.
I can think of two moments from The Dark Knight:
When Batman asks the Joker why

he wants to kill him, the Joker laughs erratically and responds, "Kill you?! I don't want to kill you! What would I do without you?... You... you... complete me." This riff on a Jerry Maguire line is both hilarious in its delivery and a little unsettling when you consider how very true it likely is. As many have said, Batman simply wouldn't be the hero he is without the Joker, and The Dark Knight does an amazing job of showcasing why that is.
The interrogation scene between Batman and Joker after he's been captured by the GCPD is amazing. It showcases how they're essentially two sides of the same coin, yet also points up their similarities in a disturbing way. They're both extremists, doing anything to further each's own cause of either chaos or order. When Batman starts beating the Joker, all the clown can do is laugh at him, pointing out that "You have nothing, nothing to threaten me with! Nothing to do with all your strength!" It's a frightening display of how much power a chaotic enough force can have over even the most delicate of circumstances, and it's that moment that Batman considers crossing the one line he's set for himself.
Again, these are just some scenes that occurred to me on first consideration of the topic. I'm sure there are plenty of others. What's your favorite Joker moment or quote? I really want to know!