Metamath Proof Explorer - Over 3000 complete formal proofs deriving numbers and beyond from Zermelo-Fraenkel set theory axioms. - http://www1.shore.net/~ndm/java/mm.html
A New System of Axioms Instead of ZF - The page claims that "the axioms shown below have the contents that should overturn the set theory of today". - http://hp.vector.co.jp/authors/VA011700/math/wardwww.htm
Extending Set Theory - Extends the language of set theory through restricted self-reference and through certain large cardinals. Also discusses higher order set theory and axiomatization through reflection principles. - http://web.mit.edu/dmytro/www/NewSetTheory.htm
Equivalence Relation - Encyclopedia entry on equivalence relations and their role in set theory. - http://www.iscid.org/encyclopedia/Equivalence_Relation
Shelah's Archive - Listing of all articles by Saharon Shelah, and links to many of them. - http://shelah.logic.at/
Axiom of Choice and Continuum Hypothesis - Part of the Frequently Asked Questions in Mathematics. - http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node34.html
Set Theory - Survey from the Stanford Encyclopedia of Philosophy by Thomas Jech. - http://plato.stanford.edu/entries/set-theory/
Cantor's Theorem - Article in the Platonic Realms, describing Cantor's diagonal argument that showed that 'infinite integers' can be ordered. - http://www.mathacademy.com/pr/prime/articles/cantor_theorem/
Operational Set Theory - Description, errata and reviews of a book by Luis E. Sanchis. - http://www.cis.syr.edu/~sanchis/operational.html
Set Theorists - A list of email addresses and affiliations. - http://www.cs.elte.hu/~kope/setad
Set Theoretic Analysis. - On a part of math where Set Theory, Topology and Analysis meet. Has surveys, preprints, conference announcements, book reviews and problems. - http://www.math.wvu.edu/~kcies/STA/STA.html
Programming with Sets - Using set-theoretic primitives as a conceptual tool in programming, includes discussion of SETL and MIRANDA languages. - http://www.cs.nmsu.edu/~complog/sets/
Bounded Set Theory - A weak version of ordinary set theory using bounded quantification. Papers and software. - http://www.botik.ru/~logic/bst/bst.html
New Foundations - Set theory introduced by W. V. O. Quine in 1937. This is a refinement of Russell's theory of types based on the observation that the types in Russell's theory look the same, as far as one can apparently prove. - http://math.boisestate.edu/~holmes/holmes/nf.html
A Crash Course in the Mathematics of Infinite Sets - A introductory guide for philosophers by Peter Suber, explaining the use of infinitary set theory. - http://www.earlham.edu/~peters/writing/infapp.htm
The Beginnings of Set Theory - MacTutor History of Mathematics topic. - http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Beginnings_of_set_theory.html
Set Theory Page - Collection of links related to set theory. - http://www.cis.syr.edu/~sanchis/setory.html
The Axiom of Choice - This page gives a brief explanation of the Axiom of Choice and links to other related websites. - http://math.vanderbilt.edu/~schectex/ccc/choice.html