You can use the border=<len> class option to increase the width of the border around the cropped output:

\documentclass[border=1pt]{standalone}
\begin{document}
$2^5 = x_5 \times y^8$
\end{document}
As in your case, the border around the image is not present in the PDF, it's from my screen capture.
It is also possible to modify this border for left/right and top/bottom border using border={<l/r> <t/b>} or for each border specifically using border={<l> <b> <r> <t>}. These options are described in the standalone documentation (section 5.2 Class options).
Incorporating Stephan Lehmke's comment, this is what the bounding boxes around the objects in the equations look like:

\documentclass[border=1pt]{standalone}
\usepackage{xcolor}
\setlength{\fboxsep}{-\fboxrule}% Remove \fbox separation for tight bounding box
\newcommand{\bbox}[1]{%
\color{red!50}\rlap{\fbox{$\phantom{#1}$}}%
\color{black}#1%
}
\begin{document}
$\bbox{2^5} = \bbox{x_5} \times \bbox{y^8}$
\end{document}
By setting \fboxsep to -\fboxrule, the outer edge of the boxes represent the bounding boxes exactly. It is now noticeable that some elements protrude outside this, causing the problems when clipping.
standalonepackage. btw, I'm getting a sufficient border by default, but maybe I have a different package version. – Stephan Lehmke Apr 25 '12 at 06:13class=articlenotarticle, but this class is the default anyway. – Martin Scharrer Apr 25 '12 at 06:25standalone. The default can be changed back in the global or a localstandalone.cfgfile. – Martin Scharrer Apr 25 '12 at 06:30