How can I display a short chapter name in the header and a long chapter name in the ToC?

\chapter[toc version]{doc version}
\chaptermark{version for header}

Helpful link with more information (also for similar or different use-cases):

http://www.tex.ac.uk/cgi-bin/texfaq2html?label=runheadtoobig

The sectioning commands of the memoir class feature a second optional argument:

\documentclass[11pt,a4paper]{memoir}

\begin{document}

\tableofcontents*% Starred form for not including the ToC in the ToC

\chapter[Title displayed in ToC][Title displayed in header]{Title}

Lorem ipsum dolor sit amet, consectetur adipiscing elit.

\clearpage\null

\end{document}

EDIT: Since v3.10, the KOMA-Script classes allow to specify the usage of the optional argument of sectioning commands. The class options are headings=optiontohead, headings=optiontotoc, and headings=optiontoheadandtoc.

\documentclass[headings=optiontohead]{scrbook}

\begin{document}

\tableofcontents

\chapter[Title displayed in header]{Title; also displayed in ToC}

Lorem ipsum dolor sit amet, consectetur adipiscing elit.

\clearpage\null

\end{document}

Another option is to use the truncate package, with fancyhdr, which truncates the header if it's too long, and adds an elypsis at the end:

 \usepackage[fit]{truncate}
 \usepackage{fancyhdr}
 \pagestyle{fancy}
 \fancyhead[RO,LE]{\truncate{.95\headwidth}{\leftmark}}
 \fancyfoot[C]{\thepage}