How can I change the alignment of a chapter/section/subsection heading? Preferably, I want this to be something I specify in the header, as this will be necessary for all headers in the document.

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This can be done using the titlesec package.

Here's a compilable demonstration example:

\documentclass{book}
\usepackage{titlesec}
\titleformat{\chapter}[display]
{20pt}{\Huge}
\titleformat{\section}
\titleformat{\subsection}
\usepackage[english]{babel}
\usepackage{blindtext}
\begin{document}
\Blinddocument
\end{document}


Now the headings are right aligned. I defined a macro \justifyheading. If you later wish to left-justify or to center, simply define \justifyheading to be \raggedleft respctively \centering.

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Just for posterity, this can be done even simpler, just using the "easy setup" technique described on 2 of the titlesec manual: just add \usepackage[raggedleft]{titlesec} to the header. –  eykanal Dec 6 '10 at 19:22
@eykanal: Great, that option really works! –  Stefan Kottwitz Dec 6 '10 at 19:32

You could use a KOMA-Script-class and redefine \raggedsection.

\documentclass{scrbook}
\renewcommand*{\raggedsection}{\raggedleft}
\usepackage[english]{babel}
\usepackage{blindtext}
\begin{document}
\Blinddocument
\end{document}

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Just for completeness -- This can also be accomplished with the sectsty package:
\usepackage{sectsty}