On a case-by-case basis you can insert a vertical strut (zero-width, vertical rule/object) to push the row contents away from others. Here's a small example:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\[
\begin{array}{|l|l|}%
\hline
& \text{Text} \\
\hline
\rule{0pt}{1.5\normalbaselineskip} & \text{Text} \\
\hline
\end{array}
\]
\end{document}
I've inserted a vertical strut of height 1.5\normalbaselineskip which is 18pt in the above example, any length exceeding the about 70% of the baseline skip would work. For more information on column and/row padding, see Column padding in tables.
Note that I've used amsmath to supply the \text command for setting text in math mode. Even though this is just a simple example and using \mbox would also suffice, amsmath also provides other functionality that is well worth using.
If you wish to insert a fixed amount (say) <len> between two rows, you can insert a blank row (with the appropriate number of column alignments & to provide correct vertical rule placement) and use a row skip of the form \\[\dimexpr-\normalbaselineskip+<len>]. This would jump "back" a length of \normalbaselineskip - the baseline distance between rows - and jump "forward" by <len> - the required gap. Here's a small example:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\[
\begin{array}[t]{|l|l|}%
\hline
& \text{Normal} \\
\hline
& \text{Text} \\
\hline
\end{array} \quad
\begin{array}[t]{|l|l|}%
\hline
& \texttt{0pt} \\
\hline
& \\[-\normalbaselineskip]
& \text{Text} \\
\hline
\end{array} \quad
\begin{array}[t]{|l|l|}%
\hline
& \texttt{2pt} \\
\hline
& \\[\dimexpr-\normalbaselineskip+2pt]
& \text{Text} \\
\hline
\end{array} \quad
\begin{array}[t]{|l|l|}%
\hline
& \texttt{1em} \\
\hline
& \\[\dimexpr-\normalbaselineskip+1em]
& \text{Text} \\
\hline
\end{array} \quad
\begin{array}[t]{|l|l|}%
\hline
& \texttt{3pc} \\
\hline
& \\[\dimexpr-\normalbaselineskip+3pc]
& \text{Text} \\
\hline
\end{array}
\]
\end{document}
arrayor increasing it? – Werner Jul 29 '12 at 13:21\addlinespacefrombooktabs. – Albert Aug 29 '18 at 12:58