I read a lot of 20th Century philosophy, and those who did the same will notice that I have left out quite a few names of well-known 20th Century philosophers, and that those I include all belong to the same analytical and empirical tradition.

The reason I have not included - say - Husserl, Heidegger, Sartre nor Marcuse or Foucault is that I don't like them at all. Also, their prose - that of Sartre too, when writing philosophically - is always boring and usually bad or very bad. (For those who disagree, I have a simple challenge: Work through Stegmüller and then explain why - say - Heidegger is worth reading, other than as an example of bad bombastic baloney. And those who like nonsense, are very much better served by e.g. Lewis Carroll - who at least knew logic and mathematics, and knew when and why he wrote nonsense, and did so very well indeed.)

Of all I will mention, Stegmüller is most recommended, because one will learn most of it. It is not original philosophy, but it is a very clear, competent and complete rendering of very much that was done in the 20th C in logic, philosophy of science, probability theory and analytical philosophy. Most of what was done in philosophy besides, at least in the West, was strongly influenced by politics (Marxism, especially) or religion (such as Thomism)

Russell: I happen to have read most that Russell published. He had a very clear mind, a very clear and pleasant style, and many interesting ideas about many subjects, and was a brave and independent individual. There is much I could recommend, but for the moment I limit myself to "The Problems of Philosophy", which is also on this side with my comments; "History of Western Philosophy", which is the only such history that made me laugh, and "Human Knowledge: Its scope and limits", which is Russell's last serious long work, and less well known than it deserves to be.

Whitehead: A. Whitehead and B. Russell cooperated on the 'Principia Mathematica', which was an attempt - very serious, in several thick volumes - to derive mathematics from logic. It failed in that the authors were forced to assume some axioms which were rather clearly of a mathematical nature, rather than a logical one, and for some other reasons, but it succeeded in laying the foundations of modern mathematical logic, and it got quite a few things in mathematical logic formulated clearly and systematically for the first time. At the time of its writing Whitehead was a pure mathematician, but later he turned to philosophy. His two most important philosophical books are "Science and the Modern World" and "Process and Reality", of which the former is far more readable than the latter, which is an interesting metaphysics of organism, but difficult to understand.

Poincaré: H. Poincaré was first and foremost a great mathematician and physicist, but he was seriously interested in philosophy, and had a very clear mind and a beautiful clear style. Three of his books from the beginning of the 20th C, that are still much worth reading and indeed, unlike most other philosophy that was published, hardly have aged, are 'La Science et l'Hypothese', 'Science et Methode' and 'La Valeur de la Science'.

Broad: Broad had a fine mind and wrote a clear style, and is less well read than he deserves to be. His most important book is "Mind - Its Place in Nature", and anybody interested at all in the subject should read it. Broad excelled in clearly analysing problems rather than in proposing new solutions, and his "Five Types of Ethical Theories" is an excellent survey.

Johnson: W.E. Johnson had some quite original and sensible ideas about logic that are contained in his "Logic" in three volumes. These volumes are not only worth reading for those interested in logic, but also for philosophy of science and semantics.

Wittgenstein: Wittgenstein produced two distinct philosophies, namely a kind of neo-positivism in the Tractatus-Logico Philosophicus and a linguistic philosophy in the Philosophical Investigations. The basic message of the two philosophies is the same: Nearly all of - non-Wittgensteinian - philosophy is nonsense: It attempts to say the unsayable by abusing language. I am not a fan of Wittgenstein, and two books that give good reasons why are Ernest Gellner's "Words and things" and J.N. Findlay's "Wittgenstein: A Critique".

Ramsey: F.P. Ramsey died before he was 30, and had a great mind. He did very fine work in philosophy, logic, the foundations of mathematics, mathematics, probability theory and economy, and his papers are collected in "Foundations of Mathematics" and "Foundations", that overlap in content but do not have the same content.

Carnap: R. Carnap was the leader of neo-positivism and a competent but not a great philosopher. Three of his books I like best are "Der logische Aufbau der Welt", "Introduction to Logic" and "Meaning and Necessity". The first attempts to give a precise and logical reconstruction of a scientific metaphysics using the tools of mathematical logic; the second is a good and clear introduction to the mathematical logic that one can find in Russell and Whitehead's 'Principia Mathematica', and has the merit of including also other things, like foundations of mereology (logical theory of wholes and parts); and the third is an attempt to surrect a theory of meaning using the tools of modal logic, which it also tries to surrect. All of these are outdated now and contain mistakes, but are well worth reading, and interesting introductions to the subjects they treat.

Reichenbach: H. Reichenbach was originally a physicist, who worked in Berlin until he had to flee Hitler's dictatorship. He is usually considered a neo-positivist, but since he knew more physics and mathematics than most neo-positivists tends to be more sensible and less dogmatical than possibly better known men like Neurath and Schlick. He publish quite a lot, including books about the foundations of probability and physics. His 'Experience and Prediction' is good.

Ayer: A.J. Ayer was British, and for the most part a follower of Russell. He got rather well-known when 26, with 'Language, Truth and Logic', which is a capable and readable summary of neo-positivism of that time. (I had my fun when 19 or 20 refuting almost all of this, but in any case it is more readable than most neo-positivist writings, though Von Mises 'Kleines Lehrbuch des Positivismus' is much better and more original.) A useful late work of Ayer is "The Central Questions of Philosophy". 

Popper: K.R. Popper is best known for two books, the last in two volumes: 'The Logic of Scientific Discovery' and 'The Open Society and Its Enemies'. In the first, he defends a philosophy of science that is based on the principle of falsifiability, i.e. a scientific theory should be falsifiable to be taken serious, as opposed to the neo-positivists who tried to base philosophy on the principle of verifiability. I think both were mistaken, but Popper less so. The other volumes are an interesting and worthwhile defense of liberalism, and an attack on totalitarianism of all kinds.

Quine: Quine was in his young years an admirer and pupil of Carnap and was American. He published rather a lot, and most was written in a contrived English style that is admired by academic philosophers. I like him far better as (philosophical) logician than as a philosopher. If you are interested in Russell and Whitehead's 'Principia Mathematica', his 'Mathematical Logic' is a fine reworking of it, and if you are interested in set theory or the foundations of mathematics, 'Set Theory and Its Logic' is nice. His best work is very probably 'Word and Object' which concerns language and meaning.

Tatarkiewicz: W. Tatarkiewicz was a Polish philosopher, and one of the few of many brilliant Poles that did not perish in the second World War. He was an admirer of Aristotle; wrote a very clear style; had a lot of knowledge; and a fair judgment. Two fine books of his are 'Analysis of Happiness' and 'The history of six ideas'. Both are histories of ideas. The first concerns ethics and the second esthetics.

Incidentally, since I mentioned many brilliant Poles: It is a great pity so very many truly intelligent Polish logicians, mathematicians and philosophers were killed between 1939 and 1945. In all three fields Poland excelled between 1900 and 1939. Much work that should have been preserved was destroyed when Warsaw was destroyed.  

Bunge: M. Bunge is an Argentinian theoretical physicist who published a lot about philosophy. His best known book is 'Causality', which is a very good summary of and introduction to the subject. Personally, I like his 'Treatise on Basic Philosophy' a lot, which is what its title says, and takes some 10 volumes. To read them with understanding requires some elementary knowledge of logic, that can be gathered from the next item. 

Stegmüller: W. Stegmüller is German, and his main work in German is in four thick volumes or quite a lot smaller volumes for students ('Studienausgabe'), and goes by the title 'Probleme und Resultate der Wissenschaftstheorie und Analytischen Philosophie' i.e. Problems and results from philosophy of science and analytical philosophy. This is an excellent summary of and introduction to these subjects, which one should not miss if one is interested in these subjects. It gives a fine survey, and explains a lot about the foundations of logic and probability that is difficult to find elsewhere.

My own view is that Russell was the most important philosopher of the 20th Century, in part because of his logical ability, in part because of his clear and pleasant style, and in part because of his wide scope, for he published 72 books about very many subjects.

The most interesting and useful books of those I mentioned are by Bunge
and Stegmüller, because they cover so much and are clearly written, by writers who were not only capable philosophers but also qualified scientifically and mathematically (indeed like Russell).