What makes this especially difficult is the vastly varying amount of time that each of these people spent as Joker. It's not easy to try to compare Hamill's time as Joker spanning around 25 years to someone who's in one movie regardless of how iconic they were in that movie.
Still giving it to Hamill despite the difficulty of the choice though. Not only is he excellent as TAS Joker, he's also excellent as the Arkham series Joker, and although he's clearly bringing a lot of the same energy to that role, they are two distinct characters, and both of them are the definitive version of Joker within their primary medium. That isn't true for any other iteration of Joker in any medium.
Although I think Hamill is the best answer, given the time disparity involved, perhaps it's worth saying that I think Ledger had the best single performance as Joker, and also that I think Monaghan probably had the single best few minutes in the role, in his very first appearance on Gotham during that last police interview/interrogation scene. That scene starts off as a routine wrap-up of an investigation and within the space of it, Monaghan's performance table-flips the tone of the episode and the character. They might not have been allowed to call him Joker, but he earned it right then anyway.
Tudyk should be on the poll instead of Leto.
Can Mark Hamil be considered? He just voices him. That's like saying voice actors should be considered for best actor awards.
If Hamill wasn't on the poll then 90% of the topic would consist of people rightly asking why Hamill wasn't on the poll.
Voice actors deserve to be considered for things like this, and I'd say that's even more true for Joker than for most other characters, and I think it's also clear how hard Hamill worked to make sure that his voice acting matched up to (and influenced) the visual portion of his animated Joker characters. Probably the single best demonstration of how good Hamill's voice acting is as a Joker characterisation is Arkham Asylum, where the Joker can't be on-screen all the time, so is constantly on the radio to his thugs and to Batman instead. That the Joker feels so twistedly and constantly present throughout that game is almost purely down to Hamill's voice work.