TITLE: Counterintuitive consequences of the Hahn-Banach theorem
QUESTION [9 upvotes]: The axiom of choice has many counterintuitive consequences like the Banach-Tarski paradox. 
The Hahn-Banach theorem is a consequence of the axiom of choice, but it is weaker. 
I would like to know some counterintuitive consequences of the Hahn-Banach theorem. 
Can the Banach-Tarski paradox be derived from the Hahn-Banach theorem?

REPLY [12 votes]: To aid future inquiries, let us record here the go-to reference kindly provided by Willie Wong in a comment above: http://consequences.emich.edu/conseq.htm. This provides a data base with a utility to search for known implications between weak forms of the axiom of choice.