List of important and influential publications in logic Wikipedia surprisingly does not contain a good list. Under philosophy of mathematics it is rather vacant too. A graduate level list is here, but I was curious more about the most influential papers. Manually one could search here. But all in all, the database out there is rather barren.
Edit: For some reason when I was typing the title it did not suggest me this math.SE question. (will delete if duplicate).
 A: All these lists are bound to be incomplete and more subjective than one would like, but a truly excellent selection of landmark papers can be found in the book "Mathematical logic in the 20th century", edited by Gerald Sacks, World Scientific, 2003. 
Here is the table of contents:


*

*The Independence of the Continuum Hypothesis. Cohen, Paul J. 

*The Independence of the Continuum Hypothesis II. Cohen, Paul J. 

*Marginalia to a Theorem of Silver. Devlin, K. I. and Jensen, R. B. 

*Three Theorems on Recursive Enumeration. I. Decomposition. II. Maximal Set. III. Enumeration without Duplication. Friedberg, Richard M. 

*Higher Set Theory and Mathematical Practice. Friedman, Harvey M. 

*Introduction to $\Pi^1_2$-Logic. Girard, Jean-Yves. 

*Consistency-Proof for the Generalized Continuum-Hypothesis. Gödel, Kurt. 

*The Mordell-Lang Conjecture for Function Fields. Hrushovski, Ehud.

*Model-Theoretic Invariants: Applications to Recursive and Hyperarithmetic Operations. Kreisel, G. 

*Recursive Functionals and Quantifiers of Finite Types I. Kleene, S. C. 

*A Recursively Enumerable Degree which will not Split over all Lesser Ones. Lachlan, A. H. 

*Measurable Cardinals and Analytic Games. Martin, Donald A.

*Enumerable Sets are Diophantine. Matijasevic, Ju. V. 

*Categoricity in Power. Morley, Michael. 

*Hyperanalytic Predicates. Moschovakis, Y. N. 

*Solution of Post's Reduction Problem and Some Other Problems of the Theory of Algorithms. Muchnik, A. A. 

*Recursively Enumerable Sets of Positive Integers and Their Decision Problems. Post, Emil L. 

*Non-Standard Analysis. Robinson, Abraham. 

*The Recursively Enumerable Degrees are Dense. Sacks, Gerald E. 

*Measurable Cardinals and Constructible Sets. Scott, Dana. 

*Stable Theories. Shelah, S. 

*The Problem of Predicativity. Shoenfield, J. R. 

*On the Singular Cardinals Problem. Silver, Jack. 

*Automorphisms of the Lattice of Recursively Enumerable Sets. Part I: Maximal Sets. Soare, Robert 

*A Model of Set-Theory in which Every Set of Reals is Lebesgue Measurable. Solovay, Robert M. 

*On Degrees of Recursive Unsolvability. Spector, Clifford.

*A Decision Method for Elementary Algebra and Geometry. Tarski, Alfred.

*Denumerable Models of Complete Theories. Vaught, R. L. 

*Model Completeness Results for Expansions of the Ordered Field of Real Numbers by Restricted Pfaffian Functions and the Exponential Function. Wilkie, A. J. 

*Supercompact Cardinals, Sets of Reals, and Weakly Homogeneous Trees. Woodin, W. Hugh. 

*Structural Properties of Models of $\aleph_1$-Categorical Theories. Zil'ber, B. I. 


(Full bibliographical details for each paper can be found in the book, of course.)
