Update
Use \arrayrulewidth
from the preamble and place it before the desired table using a group to keep the change to \arrayrulewidth
local:
\documentclass[11pt]{article}
\usepackage{array}
\begin{document}
\begin{tabular}{|l|l|l|l|}
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
\end{tabular}
\vspace{1ex}
{
\setlength\arrayrulewidth{2pt}
\begin{tabular}{|l|l|l|l|}
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
\end{tabular}
}
\begin{tabular}{|l|l|l|l|}
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
& & & \\
\hline
\end{tabular}
\end{document}

You can have individual rule control too:
For horizontal rules:
\noalign{\hrule height <length>}
instead of \hline
(you can define a command for this). For vertical rules:
!{\vrule width <length>}
instead of |
in the format specification. An example:

The code for the example:
\documentclass{article}
\usepackage{array}
\newcommand\ChangeRT[1]{\noalign{\hrule height #1}}
\begin{document}
\noindent
\begin{tabular}{
|c!{\vrule width 1pt}
c!{\vrule width 1.6pt}
c!{\vrule width 2.2pt}
c!{\vrule width 2.8pt}
c!{\vrule width 3.4pt}
c!{\vrule width 4pt}
c!{\vrule width 4.6pt}
}
\hline
& & & & & & \\
\ChangeRT{1pt}
& & & & & & \\
\ChangeRT{1.6pt}
& & & & & & \\
\ChangeRT{2.2pt}
& & & & & & \\
\ChangeRT{2.8pt}
& & & & & & \\
\ChangeRT{3.4pt}
& & & & & & \\
\ChangeRT{4pt}
& & & & & & \\
\ChangeRT{4.6pt}
\end{tabular}\par\bigskip
\noindent
\begin{tabular}{|c!{\vrule width 4pt}c|c!{\vrule width 8pt}}
\hline
column1a & column2a & column 3a \\
\ChangeRT{4pt}
column1b & column2b & column 3b \\
\hline
column1c & column2c & column 3c \\
\ChangeRT{2pt}
column1d & column2d & column 3d \\
\hline
\end{tabular}
\end{document}
The booktabs
package offers an optioanl argument to its rule commands control their thickness (vertical rules, of course, are not a good companion here):
\documentclass{article}
\usepackage{booktabs}
\begin{document}
\begin{tabular}{*{7}{c}}
\toprule[2pt]
a & b & c & d & e & f & g \\
\midrule[1pt]
a & b & c & d & e & f & g \\
\midrule
a & b & c & d & e & f & g \\
\cmidrule[2pt]{3-5}
a & b & c & d & e & f & g \\
\midrule
a & b & c & d & e & f & g \\
\bottomrule[5pt]
\end{tabular}
\end{document}
