How can I get a big cross to denote a generalized cartesian product?

Looking in the The Comprehensive LaTeX Symbol List reveals a \bigtimes symbol defined by the mathabx package.

If you don't mind using a different font, kpfonts gives you the \varprod command:

\documentclass{article}
\usepackage{kpfonts}

\begin{document}

$\varprod_{i=1}^n A_i$

\[
  \varprod_{i=1}^n A_i
\]

\end{document}

I would be more inclined to use \prod to denote a generalised cartesian product, though.

I am sure others will come up with simpler solutions, but here is an overkill solution that might be useful:

\documentclass{article}
\usepackage{amsmath}
\usepackage{tikz}
\newcommand{\Cross}{\mathbin{\tikz [x=1.4ex,y=1.4ex,line width=.2ex] \draw (0,0) -- (1,1) (0,1) -- (1,0);}}%
\begin{document}
$A \Cross B$
\end{document}

Adjust the x= and y= options to change the size, and the line width= to adjust the thickness of the line. The \mathbin ensures that correct spacing for a binary operator is placed around the symbol.