How to Rotate Text in Table across column spanning many rows

Use nested tabulars:

\documentclass[12pt]{article}
\usepackage[table]{xcolor}
\usepackage{graphicx}
\usepackage{array}
\def\Tab#1{\tabular[t]{>{\rule[-1ex]{0pt}{3ex}}c}#1\endtabular}
\newcolumntype{C}{@{}c@{}}

\begin{document}
\begin{table}[ht]
\centering
 \begin{tabular}{|C|C|C|C|C|}\hline
\Tab{Tri Sankhya \\\hline 
     Pra Trik\\Dvi Trik\\Tri Trik\\Cha Trik\\ Pan Trik\\ Shas Trik\\ Sap Trik}
&
\Tab{Vihbakti\\\hline 
     Prathama\\ Dvitiya\\Trutiya\\Chaturthi\\Panchami\\Shashthi\\Saptami}
&
\Tab{Ekavachana \\\hline
     Su (s)\\Am\\Ta (A)\\Ne (E)\\Nasi (as)\\Nas (as)\\Ni (ee)}
&
\Tab{Dvivachana\\\hline
     Au\\Aut (Au)\\Bhyam\\Bhyam\\Bhyam\\Os\\ Os}
& 
\Tab{Bahuvachana\\\hline
 \cellcolor{blue!20}
  \rotatebox{90}{~\parbox{3.5cm}{%
  Here comes the rotated text, which can also be 
  typeset in several lines.
}~}}  \\\hline
\end{tabular}
\caption{Subanta Pratyaya}
\end{table}

\end{document} 

Another possibility, regarding to your question is:

\tabular{@{}|CC|@{}}\hline% the outer one
\begin{tabular}[t]{c|c|c|c|}
 Tri Sankhya& Vihbakti & Ekavachana & Dvivachana \\\hline
  Pra Trik  & Prathama & Su (s)     & Au         \\
  Dvi Trik  & Dvitiya  & Am         & Aut (Au)   \\
  Tri Trik  & Trutiya  & Ta (A)     & Bhyam      \\ 
  Cha Trik  & Chaturthi& Ne (E)     & Bhyam      \\
  Pan   Trik& Panchami & Nasi (as)  & Bhyam      \\
  Shas Trik & Shashthi & Nas (as)   & Os         \\
  Sap Trik  & Saptami  & Ni (ee)    & Os         \\ 
\end{tabular}
&
\begin{tabular}[t]{c}
Bahuvachana\\\hline
 \cellcolor{blue!20}
  \rotatebox{90}{~\parbox{3.2cm}{%
  Here comes the rotated text, which can also be 
  typeset in several lines.
}~}
\end{tabular}\\\hline
\endtabular

but this needs to find the correct column height for the \parbox which is done in first example automatically

and a third solution, which also needs a manual setting of the parbox width:

\begin{tabular}{|c|c|c|c|>{\columncolor{blue!20}}c|}\hline
          Tri Sankhya & Vihbakti    & Ekavachana & Dvivachana & \multicolumn{1}{@{}c|}{Bahuvachana} \\
       \hline
          Pra Trik  & Prathama   & Su (s)& Au &  \\
          Dvi Trik & Dvitiya & Am & Aut (Au) &  \\
          Tri Trik  & Trutiya  & Ta (A) & Bhyam & \\ 
          Cha Trik  & Chaturthi  & Ne (E) & Bhyam & \\
          Pan   Trik & Panchami  & Nasi (as)& Bhyam &   \\
          Shas Trik & Shashthi  & Nas (as)& Os &   \\
          Sap Trik & Saptami & Ni (ee) & Os &   
  \rotatebox{90}{\makebox(0,0)[lc]{~\parbox{3.2cm}{%
  Here comes the rotated text, which can also be 
  typeset in several lines.}~}}
\\\hline
\end{tabular}

You can rotate a multi-line text using the adjustbox package. It also allows you too set the official height to zero so that you can place it in the last cell of the column where it also covers the upper cells, without interfering with the cell sizes.

For such small boxes you should use left alignment of text, best using \RaggedRight from the ragged2e package as shown.

\documentclass[fleqn,12pt,a4paper]{article}
\usepackage{tabularx}
\usepackage[table]{xcolor}
\usepackage{adjustbox}
\usepackage{ragged2e}
\begin{document}
  \begin{table}[ht]
    \def\C{\cellcolor{blue!50}}
    \begin{minipage}[b]{1 \linewidth}\centering
      \begin{tabular}{|c|c|c|c|c|}
      \hline
        Tri Sankhya & Vihbakti & Ekavachana & Dvivachana & Bahuvachana \\
      \hline
        Pra Trik    & Prathama & Su (s)     & Au & \C  \\
        Dvi Trik    & Dvitiya  & Am         & Aut (Au) & \C  \\
        Tri Trik    & Trutiya  & Ta (A)     & Bhyam & \C \\ 
        Cha Trik    & Chaturthi& Ne (E)     & Bhyam & \C \\
        Pan Trik    & Panchami & Nasi (as)  & Bhyam & \C  \\
        Shas Trik   & Shashthi & Nas (as)   & Os & \C  \\
        Sap Trik    & Saptami  & Ni (ee)    & Os & \C
        \adjustbox{minipage=3.2cm,angle=90,raise={1pt}{0pt}{0pt}}{% raise by 1pt, set height and depth to 0pt.
            \RaggedRight
            Here comes the rotated text, which can also be 
            typeset in several lines.
        }
        \\
      \hline
      \end{tabular}
      \caption{Subanta Pratyaya}
    \end{minipage}
  \end{table}
\end{document}