If you would like to have this "continued" heading in the body text, as heading above the continued table of contents, you can use the afterpage package. Here's an example:
\documentclass{report}
\usepackage{afterpage}
\DeclareRobustCommand*{\contheading}{%
\afterpage{{\normalfont\large\bfseries\centering
Table of Contents - Continued\par\bigskip}}}
\begin{document}
\addtocontents{toc}{\contheading}
\tableofcontents
\chapter{One}
...
\chapter{Twenty}
\section{One}
\chapter{Twenty one}
\section{One}
...
\end{document}

Here I defined a macro \contheading which prints our text on the following page. That command will be written to the .toc file, where \tableofcontents can read it. To protect this command, so that it's written to the .toc file without being expanded, I used \DeclareRobustCommand.
If there are more pages of the table of contents, you can repeat adding \contheading at the appropriate places. This can be error prone sdince you could forget a page if there are lots of them and an approach using header entries might be more suitable.
If you don't want the heading in the body text, but in the page header, use features of your class or your headings package, such as fancyhdr or scrlayer-scrpage. Then, for example, \markboth is useful to override the existing header entry:
\newcommand*{\contheading}{Table of Contents - Continued}% in the preamble
...
% later at the beginning of the text:
\addtocontents{toc}{\protect\markboth{\contheading}{\contheading}}
Here I used \protect to prevent the expansion of \markboth when it's written to the .toc file.
Here's a complete example:
\documentclass{report}
% Some general header style settings:
\usepackage{fancyhdr}
\fancyhf{}
\renewcommand{\headrulewidth}{0pt}
\fancyhead[C]{\leftmark}
\pagestyle{fancy}
% The text of our heading:
\newcommand*{\contheading}{Table of Contents - Continued}
\begin{document}
% Now we write the command to the TOC:
\addtocontents{toc}{\protect\markboth{\contheading}{\contheading}}
\tableofcontents
\chapter{One}
...
\chapter{Twenty}
\section{One}
\chapter{Twenty one}
\section{One}
...
\end{document}
fancyhdrpackage would help? – mbork Jul 23 '11 at 18:37