Start new chapter on same page

The \chapter command internally uses \cleardoublepage and \clearpage to add page breaks. Use the etoolbox package to selectively change the definition of \chapter.

\documentclass{book}

\usepackage{etoolbox}
\makeatletter
\patchcmd{\chapter}{\if@openright\cleardoublepage\else\clearpage\fi}{}{}{}
\makeatother

\begin{document}

\chapter{foo}

Some text.

\chapter{bar}

Some text.

\end{document}

Note: This etoolbox hack also works for the report class.

For KOMA-Script scrbook from version 3.19a (and most likely for other KOMA-Script classes, too), you need to patch \scr@startchapter instead of chapter:

\usepackage{etoolbox}
\makeatletter
\patchcmd{\scr@startchapter}{\if@openright\cleardoublepage\else\clearpage\fi}{}{}{}
\makeatother

\documentclass{report}
\begin{document}

\chapter{foo}

{\let\clearpage\relax \chapter{bar}}
\chapter{baz}
\end{document}

use \cleardoublepage instead of \clearpage for a two sided document

I have used this whenever I needed to add one chapter to the previous page:

\begingroup
\let\clearpage\relax
\chapter{My Chapter}
\endgroup

It doesn't change the rest of the chapters, or anything else in the document.