There are three definitive visions of Batman's nemesis, The Joker: Jack Nicholson's, Mark Hamill's, and Heath Ledger's.
I realize this sounds like a bit of a contradiction in terms. And yet, who would really argue against it?* Nicholson's joker breathed fresh life into a moribund franchise, bringing a bit of sadistic glee and a panache of class to a genre that was often lacking in both. It was a reminder that superhero films are only as good as their villains, and for a long time Nicholson's maniacal grinning goon—id unleashed—was about as good as it got.
Mark Hamill, meanwhile, put his own stamp on the Batman's arch villain during his beloved run on Batman: The Animated Series. Hamill's voice work on the mid-90s Fox cartoon gave the Joker a whole new edge: the terrifying laugh, the alternations in pitch, the breakneck shifts from gleeful evil to a darker-edged psychotic bark. I can't read a comic book in which the Joker appears without hearing Hamill's voice.
Indeed, pretty much the only reason to pick up the DC Animated Universe's release of The Killing Joke is to experience the nostalgia-rush of hearing Hamill voice the Clown Prince of Crime one last time. The first half-hour of the film tells a new story about Batgirl, explaining why she quit her gig as Batman's sidekick. The last hour is a more-or-less perfectly faithful retelling of the classic Alan Moore/Brian Bolland; so faithful, in fact, that one wonders if the whole exercise isn't a bit superfluous. It's more transliteration than translation, saved only by the fact that Hamill is so damn good in the role.
Finally, of course, you have Heath Ledger's Joker, a performance so commanding that it earned Ledger a posthumous Oscar. Ledger's Joker was part Tom Waits, part Chicago thug, part junkie philosopher: terrifying, but not quite the agent of chaos he claimed to be. Whereas Nicholson and Hamill were all id, there's very much a purpose behind the Joker that Ledger and director/writer Christopher Nolan brought to life.
I realized toward the end of my Suicide Squad review that I hadn't once mentioned Jared Leto's performance as the Joker. After a moment's thought, I decided not to go back and work in a mention. In part, that's because he is almost wholly superfluous to the plot: you need the Joker to understand Harley Quinn's (Margot Robbie) specific brand of madness and motivation, but not much else. Even if he had a bigger role, Leto's interpretation of the character is decidedly ... okay. He's scary in a crazy sort of way and you can tell Leto put a lot of work into the role. But, that's part of the problem: you can tell it's a role. Leto's voice is a bit too close to Ledger's and director David Ayer cribs from iconic imagery, like this Alex Ross painting, that doesn't quite fit Leto's street hood vision of the character. Leto simply doesn't make the part his own.
In other words, Leto's version of the Joker is not definitive. And with so many other, better options to choose from, why waste words on it?
*Indeed, I bet more people would argue that the total is actually four, citing Romero's Joker, than would argue you can't have multiple definitive versions of a single character.