How do I remove "Chapter N" from the chapter titles of a book

With the help of titlesec:

\documentclass{book}
\usepackage{titlesec}
\usepackage{lipsum}

\titleformat{\chapter}[display]
  {\normalfont\bfseries}{}{0pt}{\Large}

\begin{document}

\chapter{Test Chapter}
\lipsum[3]

\end{document}

Without titlesec:

\documentclass{book}
\usepackage{lipsum}

\makeatletter
\def\@makechapterhead#1{%
  \vspace*{50\p@}%
  {\parindent \z@ \raggedright \normalfont
    \interlinepenalty\@M
    \Large \bfseries #1\par\nobreak
    \vskip 40\p@
  }}
\def\@makeschapterhead#1{%
  \vspace*{50\p@}%
  {\parindent \z@ \raggedright
    \normalfont
    \interlinepenalty\@M
    \Large \bfseries  #1\par\nobreak
    \vskip 40\p@
  }}
\makeatother
\begin{document}

\chapter{Test Chapter}
\lipsum[3]

\end{document}

To customize the headers/footers, one option is to use the fancyhdr package; a little example, suppressing the prefix "Chapter N" from the default headers, and with the text in normal case (no upper-case):

\documentclass{book}
\usepackage{titlesec}
\usepackage{fancyhdr}
\usepackage{lipsum}

\titleformat{\chapter}[display]
  {\normalfont\bfseries}{}{0pt}{\Large}

\pagestyle{fancy}

\fancyhf{}
\fancyhead[RE]{\leftmark}
\fancyhead[LO]{\rightmark}
\fancyhead[LE,RO]{\thepage}
\renewcommand\headrulewidth{0pt}
\renewcommand\chaptermark[1]{\markboth{#1}{}} 
\renewcommand\sectionmark[1]{\markright{\thesection.\ #1}}

\begin{document}

\chapter{Test Chapter}
\section{Test Section}
\lipsum[1-20]

\end{document}

Another option for the headers/footers is to use the pagestyles option for titlesec and design the desired style:

\documentclass{book}
\usepackage[pagestyles]{titlesec}
\usepackage{fancyhdr}
\usepackage{lipsum}

\titleformat{\chapter}[display]
  {\normalfont\bfseries}{}{0pt}{\Large}
\newpagestyle{mystyle}{
  \sethead[\thepage][][\chaptertitle]{\thesection~\sectiontitle}{}{\thepage}
}
\pagestyle{mystyle}

\begin{document}

\chapter{Test Chapter}
\section{Test Section}
\lipsum[1-20]

\end{document}

Partial solution

Thanks to einpoklum's answer, I found that this

\titleformat{\chapter}[display]
{\bfseries\Large}                                            
{\filright}
{1ex}{}[]

solves the problem for the chapter start.

But the page headers remain.

Full solution

It appears this did it. Thanks to Gonzalo Medina, for his answer, from where I exerted the code.

\usepackage[pagestyles]{titlesec}
\titleformat{\chapter}[display]{\normalfont\bfseries}{}{0pt}{\Huge}
\newpagestyle{mystyle}
{\sethead[\thepage][][\chaptertitle]{}{}{\thepage}}
\pagestyle{mystyle}

Now it looks the way I like. (The screenshots got dusty, for some reason.)

chapter http://user.it.uu.se/~embe8573/chapter.png header http://user.it.uu.se/~embe8573/header.png

The 'Chapter N' text is the value of the \@chapapp macro, defined in the book document class.

But... no need to tinker with that directly. See

How to create specific chapter style in book documentclass

it refers you to the titlesec package and to these pages, with which you can change the chapter heading style. One of the things you can do, specifically, is play with the way the number is displayed.