You can define a new command which changes the value of \arrayrulewidth, draws the \cline and then restores \arrayrulewidth to its original value:
\documentclass{book}
\newlength{\Oldarrayrulewidth}
\newcommand{\Cline}[2]{%
\noalign{\global\setlength{\Oldarrayrulewidth}{\arrayrulewidth}}%
\noalign{\global\setlength{\arrayrulewidth}{#1}}\cline{#2}%
\noalign{\global\setlength{\arrayrulewidth}{\Oldarrayrulewidth}}}
\begin{document}
\begin{tabular}{ccc}
a & b & c \\\Cline{2pt}{2-3}
d & e & f \\\Cline{3pt}{1-2}
\end{tabular}
\end{document}

The first argument of \Cline controls the "thickness" of the rule.
EDIT: The \cmidrule command provided by the booktabs package admits an optional argument controlling the thickness of the rule, so you can say:
\documentclass{book}
\usepackage{booktabs}
\begin{document}
\begin{tabular}{ccc}
a & b & c \\ \cmidrule[2pt]{2-3}
d & e & f \\ \cmidrule[3pt]{1-2}
\end{tabular}
\end{document}
\multirowcommand from the multirow package. – O. R. Mapper Dec 19 '14 at 09:57mathtoolspackage, this doesn't seem to work... any ideas? – cmhughes Mar 15 '15 at 18:15
– Francisco Jun 07 '18 at 12:23booktabsis a good solution, provided you don't use vertical lines, which the package creator refuses to implement.