How to divide LaTeX table cells vertically?

You can achieve this with the hhline package:

\documentclass{article}
\usepackage{hhline}
\begin{document}
\begin{tabular}{|c||c||c||c|}
  \hhline{|--||-||-|}
  \multicolumn{2}{|c||}{First Cell}&
  Second Cell&
  Third Cell\\
  \hhline{=:t:=::=::=:}
  \begin{tabular}{@{}l@{}} Data\\ Data\\ Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}\\
  \hhline{=::=::=::=:}
  More data &
  More data &
  More data &
  More data\\
  \hhline{|-||-||-||-|}

\end{tabular}
\end{document}

\documentclass{article}

\usepackage{array,hhline}

\begin{document}

\setlength\extrarowheight{2pt}
\begin{tabular}{|c||c||c||c|}
  \hhline{|--||-||-|}
  \multicolumn{2}{|c||}{First Cell}&
  Second Cell&
  Third Cell\\
  \hhline{=:t:=::=::=}
  \begin{tabular}{@{}l@{}} Data\\ Data\\ Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}&
  \begin{tabular}{@{}l@{}}
    Data\\
    Data\\
    Data\\
  \end{tabular}\\
  \hhline{|-||-||-||-|}
\end{tabular}

\end{document}