TikZ labelling venn diagram

A simple solution is

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
  \tikzset{venn circle/.style={draw,circle,minimum width=6cm,fill=#1,opacity=0.4}}

  \node [venn circle = red] (A) at (0,0) {$A$};
  \node [venn circle = blue] (B) at (60:4cm) {$B$};
  \node [venn circle = green] (C) at (0:4cm) {$C$};
  \node[left] at (barycentric cs:A=1/2,B=1/2 ) {$A \cap B$}; 
  \node[below] at (barycentric cs:A=1/2,C=1/2 ) {$A \cap C$};   
  \node[right] at (barycentric cs:B=1/2,C=1/2 ) {$B \cap C$};   
  \node[below] at (barycentric cs:A=1/3,B=1/3,C=1/3 ){$A \cap B \cap C$};
\end{tikzpicture}  
\end{document}

\documentclass{article}
\usepackage{pst-node}   
\SpecialCoor

\usepackage[active,tightpage]{preview}
\PreviewBorder=0pt\relax
\PreviewEnvironment{pspicture}

\begin{document}

\begin{pspicture}(-3.25,-3.25)(3.25,3.25)
  \def\R{1}
  \def\RR{2}    
  \pnode(\R;30){A}\rput(\RR;30){$A$}
  \pnode(\R;150){B}\rput(\RR;150){$B$}
  \pnode(\R;270){C}\rput(\RR;270){$C$}
  \psset{opacity=0.4}
  \def\r{2}
  \pscircle*[linecolor=red](A){\r} 
  \pscircle*[linecolor=green](B){\r} 
  \pscircle*[linecolor=blue](C){\r}
  \def\d{1.5}
  \rput(\d;90){$A \cap B$}
  \rput(\d;210){$B \cap C$}
  \rput(\d;-30){$A \cap C$}  
  \rput(0,0){$A\cap B\cap C$}
\end{pspicture}

\end{document}

You could place the labels manually by using \node at (<x>,<y>) {$A \cap C$};, but you'd have to find the coordinates by trial and error.

A more "proper" way is using the intersections library. To use it, you name the paths you want to intersect using unique names (name path=<name>), in this case the circles.

Then you can find the intersections by issuing name intersections = {of=<firstpath> and <secondpath>} as an argument to a path or a draw command.

The intersections will be available as coordinate nodes with the naming scheme intersection-<number>. You can now define a path between two intersections, and place a node halfway between the intersections using node [pos=0.5] {<label>} in the path.

For labelling the central overlap, you could use the calc library to specify the average of the circle coordinates using ($0.33*(A)+0.33*(B)+0.33*(C)$):

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections}
\usetikzlibrary{calc}


\begin{document}

\def\firstcircle{[name path=firstcircle] (0,0) circle (2cm)}
\def\secondcircle{[name path=secondcircle] (55:2.67cm) circle (2cm)}
\def\thirdcircle{[name path=thirdcircle] (0:3cm) circle (2cm)}

% Now we can draw the sets:
\begin{tikzpicture}
    \draw \firstcircle node[below,name=A] {$A$};
    \draw \secondcircle node [above,name=B] {$B$};
    \draw \thirdcircle node [below,name=C] {$C$};
    \path [ name intersections = {of = firstcircle and secondcircle } ] (intersection-1) -- (intersection-2) node [pos=0.5] {$A \cap B$};
    \path [ name intersections = {of = secondcircle and thirdcircle } ] (intersection-1) -- (intersection-2) node [pos=0.5] {$B \cap C$};
    \path [ name intersections = {of = firstcircle and thirdcircle } ] (intersection-1) -- (intersection-2) node [pos=0.5] {$A \cap C$};
    \node at ($0.33*(B)+0.33*(C)+0.33*(A)$) {$A \cap B \cap C$};
\end{tikzpicture}

\end{document}