That would probably be Kant because he made Transcendental Idealism respectable, and laid the foundation for science and no one has gotten past those foundations that he laid yet as far as I know.

Most art is self indulgent. It is produced by the self to express the self either to the self or others. So somehow if the artist is not indulging the self then then there is little to express. I would say that indulgent art is allopoietic in the sense that it is producing something other than one’s authentic self. But good art is autopoietic in the sense that it is genuinely producing the self qua self which is the unique individuation of the artist. But of course this is just a guess. What it means to be  “self” indulgent is open to interpretation. But art qua art is an expression of the self no matter how abstract or minimalistic or conceptual we attempt to be. Good art is not just a self-expression but also is archetypal in some sense. As Kant says Beauty is intersubjective in some sense. Great art hits a chord we all can appreciate somehow, or at least ought to appreciate to the extent we realize our humanity within ourselves.

To me the art of Bacon that Deleuze praises is self-indulgent. I don’t see what Deleuze sees in it.

But for instance the statue of Laocoon cannot ever be called Self-indulgent because the self that expressed it expressed purely the human condition. The self of the artist is effaced in its immersion in the human condition. But by that it does not lose its individuality, but instead heightens it to embrace everyone somehow  which is what Jung calls the individuation of the self.

Kant in his Critiques. He really started it all in the modern period.

David Bohm See http://en.wikipedia.org/wiki/Bohm_Dialogue

What is the use of listing names? It is kinda silly since we can just go to wikipedia and get those lists. And Nine, forget any specific number because there have been thousands, but the some of the names listed in other answers are significant. The question is what is it that makes a thinker on logic’s work influential. What are the criteria? The main criteria is that they should profoundly change how we think about logic. Best example is Peirce. He has probably done more to change the way we think about logic than anyone else since Aristotle who created it for us in the West. But there has been so much work in logic over the last century that it is difficult to say who is most important. Fuzzy Logic is definitely important. Para-consistency of Priest is important. But perhaps the most important is G. Spencer Brown who along with Bricken and Hellerstien and Kauffman have created a boundary logic that is the logic of Masses to rival the Syllogistic Logic of Sets. But then also very important is August Stern and his Matrix Logic. There are now myriad deviant logics including Quantum Logic that are significant. Another major contribution was Higher Logical Type Theory of Russell. But also Wittgenstein’s Tractatus and his later retraction Philosophical Investigations and Philosophical Grammar drew a lot of attention to logic. Also there is Topos theory, which is about the Categorical representation of logic. There has been a lot happening in Logic over the last century. Logic is not what you think it is anymore. It is a whole field with multiple profound contributions. No standard list of names is going to capture that reality. A renaissance in Logic has occurred over the last century and everyone basically missed it. But eventually it will change the way we think about everything. An important contribution to this was the book Life Itself by Robert Rosen where he shows that causal and inference structures can be analyzed categorically into entailment structures and that these are more complex than we bargained for, complex enough to let biology into the science that includes physics without appeal to vitalism. Lots going on there to learn about, think about and use as a tool for making our theorizing better.

Zizek talks about Ethical Evil which Kant did not believe existed.

Easy to list them, but hard to say why they are influential. They are influential because they are exploring the ideas of Heidegger based on those of Husserl, Hegel and Aristotle. They have rediscovered the meta-levels of Being. They have explored this territory discovering

Pure Being – Husserl
Process Being — Heidegger
Hyper Being — Heidegger, Merleau-Ponty, Derrida
Wild Being — Merleau-Ponty, Deleuze, Castoradis
Ultra Being — Zizek, Badiou

If you can understand these kinds of Being you can understand the nature of the essential nature of the Western worldview.

Zizek is the most influential because he is like a pop star of philosophy due to the fact that he has an opinion on everything. But he also has some deep points to make especially when you contrast him with Badiou and understand his reduction of Lacan to Hegel. He is appealing because he has interesting things to say about everything under the sun. He likes to say things that are controversial and thrives on intellectual jousting with the other intellectual pop stars of our time.

Probably Zizek’s books particularly Parallax View but the other significant ones as well all work together to give an interesting reevaluation of Hegel now that Marxism is free from the Soviet Communist yoke. The first such book was Critique of Dialectical Reason by Sartre. Recent books by Fredrick James are also offering reassessment of dialectics in the face of Postmodernism. But Zizek has actually via Lacan come up with a genuinely new view of Hegel and if taken seriously that is going to make a difference in the way political philosophy is understood. The first big break was the political economics of Bataille with the idea of the Accursed Share. We can see the effects of that in Deleuze and Baudrillard. But Zizek uses Lacan and Hegel to drive the point home with a vengeance which should transform the way we think about politics fundamentally in terms of the blatant Ideology of our supposedly post-ideological age after a century of ideological warfare. Just because you have beaten all ideological foes does not mean Ideology has vanished, it has just gone underground because there are no other standing ideologies to compete any longer. Zizek makes the point that unconscious ideology is probably worse than blatant ideological discourse because everyone thinks they are free from ideology.

They are really all sophists, even Socrates.