Logo situated only on titlepage of Beamer presentation

You can use

\title[Title]{Title\\[1em]\includegraphics[width=3cm]{logo}}

it's important to use the optional argument with the title once again so the right title would be used in other parts of the document (foot/headline, for example).

Another option would be to redefine the title page template to include the logo in the desired position:

\makeatletter
\setbeamertemplate{title page}
{
  \vbox{}
  \vfill
  \begin{centering}
    \begin{beamercolorbox}[sep=8pt,center]{title}
      \usebeamerfont{title}\inserttitle\par%
      \vskip0.25em%
      {\usebeamercolor[fg]{titlegraphic}\inserttitlegraphic\par}
      \ifx\insertsubtitle\@empty%
      \else%
        \vskip0.25em%
        {\usebeamerfont{subtitle}\usebeamercolor[fg]{subtitle}\insertsubtitle\par}%
      \fi%     
    \end{beamercolorbox}%
    \vskip1em\par
    \begin{beamercolorbox}[sep=8pt,center]{author}
      \usebeamerfont{author}\insertauthor
    \end{beamercolorbox}
    \begin{beamercolorbox}[sep=8pt,center]{institute}
      \usebeamerfont{institute}\insertinstitute
    \end{beamercolorbox}
    \begin{beamercolorbox}[sep=8pt,center]{date}
      \usebeamerfont{date}\insertdate
    \end{beamercolorbox}\vskip0.5em
  \end{centering}
  \vfill
}
\makeatother

and then simply use \titlegraphic:

\titlegraphic{\includegraphics[width=3cm]{logo}}

As a logo is usually associated with an organization, I use the \institute macro to put the logo on title frame:

\institute[short name]{\includegraphics[width=3cm]{logo}}

(short name is usually printed on every slide depending on the theme used.)

But this logo is not between title and subtitle... The default order is the following:

\documentclass{beamer}
\title{title}
\subtitle{subtitle}
\institute{institute}
\author{author}
\date{date}
\titlegraphic{titlegraphic}
\begin{document}
\begin{frame}
  \maketitle
\end{frame}
\end{document}

A simple solution is this:

\title{title}
\author{authorname}
\institute{\includegraphics[scale=0.035]{logo} \\Physics Department\\ IIT Bombay}