I'm going to mainly talk about Heath Ledger's style of joker, the whole "mad-man" portrayal rather than the criminal mastermind type. The Joker is seen as a man of Chaos, Anarchy if you prefer that word, but you may be surprised that there is more Order and Justice in the Joker than there is in Batman.
There is an assumption that The Joker is some kind of Nihilist, and this would be correct to an extent, but Joker takes Nihilism to a whole new level. He isn't just a Nihilist, He's a Discordian Nihilist. Discordian Nihilists are basically all the forms of Nihilism rolled into one, with a almost comical amount of Irony to the logic. To Discordian Nihilists, its not just that life is meaningless, or lacks any real meaning, but the meaning that you can get as a Nihilist is almost laughable. A Discordian Parable would go something like this
"If a gong is a sign of Enlightenment, a gong is just two pieces of metal hitting each other, thus if you are at a traffic light you must just go whenever you want, because even if you get hit by another car you aren't just dead you are enlightened"
As for the Joker's Political Philosophy, like i said there is much more order in his logic than you would immediately think. He is an Anarchist, but not in the sense that Anarchism has come to mean "Chaos" and "Disorder" its actually quite the opposite, his form of Anarchism is underpinned by Order, but an order of disorder. Disorderly thinking, he is an Egoist, Egoism is basically intertwined with Nihilism, in accordance to Max Stirner's work on Egoism; Egoism is the Fundamental belief that all hierarchy is unjustified including ethics, morals, cultural and societal norms.
The Joker is not a man without morals or empathy, he is a man of vengeance rather than justice. Since Justice follows some kind of moral rule book, whilst vengeance doesn't really have to. The Joker rarely looks at the people whom he kills or injures, and when he said "If you are good at something, never do it for free" he doesn't always mean it in a monetary sense, you can tell from almost every movie that money means absolutely nothing to him. He doesn't guard it, he flings it around anytime he has it, and sets fire to a mountain of it to make a point. When he says that famous line he doesn't mean monetary at all, it's worth noting that the Joker has henchmen, those men and women owe him a favour and you could say they owe them their life for whatever he has done for them. So when he makes that point what he's really saying is "if you are good at something, surround yourself with people who will reciprocate that greatness". A reciprocal dynamic that is inherent to consistent Anarchism, the idea of Mutual Aid, the Idea that if you are good at something and another person needs that talent, then do it, not for monetary benefit, but both because you want to and because that person has something to offer you; Mutual aid for Mutual gratification.
This won't be a surprise to you but Bane is the more streamlined logical form of Anarchist in comparison to the Joker. Bane is the Academic to the Joker's High school based edge. Bane's Philosophy is one based on the idea that Gotham has been cheated out of potential greatness, that there are too many people on top each other for anything meaningful to get done. But of course, Bane has a destructive edge to him. Finding a Atom bomb and killing the only man that can disarm it in front of the whole city. But on the other hand, Bane means well in his metaphor, he want's to get rid of the old so that those in the city can rebuild something worthwhile. But of course with very disorderly thinking.
Bane has a Revolutionary background through his father and these beliefs likely came from serving time in Prison and through his father (King Snake). Much of Bane's internal Philosophy is akin to the Joker's apart from the difference that Bane see's a meaning to his life, Bane is actively pursuing Anarchy whilst the Joker is just a mere embodiment of it.
Bane and the Joker have a deep hatred for Batman, and its not just because Batman is a good arch nemesis for them to have. Batman serves as a living embodiment of everything they are both against as Anarchist's, he is a rich man who has gotten his power through other people's work, and fights for justice whilst leaving everyone less fortunate than him at the bottom. When the Joker talks about not wanting to kill Batman to his face he is correct in his sentiment that the Joker and Batman "need eachother" to survive. The Joker and Batman, Bane and Batman, they are each other's Ying to their Yang. One has to exist for the other to, to put a finer Political point, its like in the Historical Dialectic of Marx in that, In order for Communism to exist, Capitalism had to have come before. Otherwise, how would those in Communism know what to be against without having a visual representation of it, same thing with Bane, Joker and Batman.