One possibility is to redefine the command \chaptername. Here is a minimal working example:
\documentclass{amsbook}
\renewcommand{\chaptername}{}
\begin{document}
\tableofcontents
\chapter{My great chapter}
\end{document}
For more advanced customization, you may also be interested in packages such as titlesec. Note that there may also be customization possibilities built-in the amsbook class that I am not aware of (for instance memoir provides such abilities).
EDIT: as noted in the comments, one should in fact be a little more careful because of the presence of an \enspace in @makechapterhead in the class amsbook.cls. Perhaps the best option to redefine the @makechapterhead command as a whole is to use etoolbox, as egreg suggests:
\usepackage{etoolbox}
\makeatletter
\patchcmd{\@makechapterhead}{\uppercase\@xp{\chaptername}\enspace}{}{}{}
\makeatother
\renewcommand{\chaptername}{}? – Corentin Nov 06 '12 at 21:45