A good compromise is usually \centernot (from the package centernot).
But sometimes \centernot is good, sometimes it isn't. For instance, \centernot{\in} produces a poorer result than \notin that uses the common slash instead.
In other cases, some small adjustments are necessary:
\documentclass{article}
\usepackage{centernot}
\begin{document}
$\centernot{\eta}$
$\mkern-1mu\not\mathrel{\mkern1mu\eta}\mkern1mu$
\end{document}

The first \mkern does a small backing up; then \not is typeset, which takes no horizontal space, then \eta is printed with no intervening space, because it has been turned into a relation symbol and TeX adds no space between consecutive relation symbols, but preceded by a small space that compensates for the negative space inserted before. A final space is added to take care of the fact that the slash ends right of \eta.
Note that all the construction will be considered as a relation symbol as far as spacing is concerned:
\documentclass{article}
\newcommand{\noteta}{%
\mkern-1mu\not\mathrel{\mkern1mu\eta}\mkern1mu
}
\begin{document}
$A \noteta B$
\end{document}

If an ordinary symbol is desired, add \mathord or just a pair of additional braces:
\newcommand{\noteta}{%
\mathord{\mkern-1mu\not\mathrel{\mkern1mu\eta}\mkern1mu}%
}
is equivalent to, but clearer than,
\newcommand{\noteta}{%
{\mkern-1mu\not\mathrel{\mkern1mu\eta}\mkern1mu}%
}
Such manual adjustments may be needed depending on the shape of the symbols involved.
\not\modelswork for you? – Scott H. Oct 27 '13 at 18:06\notin front of they symbol to be negated. – Scott H. Oct 27 '13 at 18:10\not. – Scott H. Oct 27 '13 at 18:15\cancel,\not, and more? – Werner Oct 27 '13 at 18:25