Tables: subtables; figures: subfigures

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}

Further reading