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If using the subfigure package, leaving a blank line between the subtables will make Latex put all the tables (or figures) in a vertical column. If you do not leave spaces, the tables or figures will be placed side-by-side if there is enough room, as expected.
Thus:
\documentclass[a4paper,12pt]{article}
\usepackage{booktabs}
\usepackage{subfigure}
\begin{document}
\begin{table}[tbp]
\centering
\caption{The desired result}
\label{fnru435n}
\subtable[Title of subtable]{
\begin{tabular}{lll}
\toprule
header 1 & header 2 & header 3 \\
\midrule
column 1 & column 2 & column 3 \\
\bottomrule
\end{tabular}
\label{h5ft5nb}
}
\subtable[Title of subtable]{
\begin{tabular}{lll}
\toprule
header 1 & header 2 & header 3 \\
\midrule
column 1 & column 2 & column 3 \\
\bottomrule
end{tabular}
\label{h5ft5na}
}
\end{table}
\end{document}
not:
\documentclass[a4paper,12pt]{article}
\usepackage{booktabs}
\usepackage{subfigure}
\begin{document}
\begin{table}[tbp]
\centering
\caption{Not the desired result}
\label{fnru435f}
subtable[Title of subtable]{
\begin{tabular}{lll}
\toprule
header 1 & header 2 & header 3 \\
\midrule
column 1 & column 2 & column 3 \\
\bottomrule
\end{tabular}
\label{h5ft5fb}
}% The next line is blank
\subtable[Title of subtable]{
\begin{tabular}{lll}
\toprule
header 1 & header 2 & header 3 \\
\midrule
column 1 & column 2 & column 3 \\
\bottomrule
\end{tabular}
\label{h5ft5fa}
}
\end{table}
\end{document}
