page numbering in table of contents

I don't think it's a good idea, but I know that some institutions have crazy requirements.

If you only need plain lowercase roman numerals, it's easy. See the comment in the code.

I also added a simpler solution for the problem of getting “really empty pages”: load the emptypage package. Also, \pagenumbering{arabic} should be issued before the first chapter.

\documentclass[11pt,a4paper,openright,twoside]{report}

\usepackage{emptypage}

\begin{document}

\begin{titlepage}
This is the title page
\mbox{}
\end{titlepage}

\cleardoublepage
\pagenumbering{roman} 

\begin{center}
\large\bfseries Abstract
\end{center}

Abstract text

\cleardoublepage
% Let's change \thepage so it prints one less than
% the real page number; \pagenumbering{arabic}
% will redefine it to the right meaning afterwards.
\renewcommand\thepage{\romannumeral\numexpr\value{page}-1\relax}

\tableofcontents

\cleardoublepage
\pagenumbering{arabic}
\chapter{First chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Second chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Third chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Fourth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Fifth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Sixth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Seventh chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Eight chapter}
\section{First section}
\section{Second section}
\section{Third section}
\end{document}

It's more complicating than one can think at a first glance...

First of all, remove the option openright when loading the document class and load the package etoolbox.

Then insert \setcounter{page}{2} just before \tableofcontents.

At this point insert the following lines just after the first chapter:

\patchcmd{\chapter}
  {\clearpage}
  {\cleardoublepage}
  {}
  {}

Note that \setcounter{page}{1} after \pagenumbering{arabic} is not needed and \cleardoublepage can be redefined in a simple manner:

\let\origdoublepage\cleardoublepage
\renewcommand{\cleardoublepage}{%
  \clearpage
  {\pagestyle{empty}\origdoublepage}%
}

MWE:

\documentclass[11pt,a4paper,twoside]{report}
\usepackage{etoolbox}

% Fixing the appearance of the footer in the empty pages in between chapters.
\let\origdoublepage\cleardoublepage
\renewcommand{\cleardoublepage}{%
  \clearpage
  {\pagestyle{empty}\origdoublepage}%
}
% Finished fixing appearance

\begin{document}

\begin{titlepage}
This is the title page
\mbox{}
\end{titlepage}

\cleardoublepage
\pagenumbering{roman} % Yay, roman numbering (i, ii, iii, iv) for the abstract and table of contents.
\begin{center}
\subsection*{Abstract}
\end{center}
Abstract text

\cleardoublepage
\setcounter{page}{2}
\tableofcontents

\chapter{First chapter}
\pagenumbering{arabic} % And moving back to arabic numbering (1,2,3,4) for the body.
\patchcmd{\chapter}
  {\clearpage}
  {\cleardoublepage}
  {}
  {}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Second chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Third chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Fourth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Fifth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Sixth chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Seventh chapter}
\section{First section}
\section{Second section}
\section{Third section}

\chapter{Eight chapter}
\section{First section}
\section{Second section}
\section{Third section}
\end{document}  

Output: