At its heart the alignat environment is built on TeX's \halign. In that environment you can ignore the formatting specifications for a given column by issuing \omit. Thus writing
\omit\hfill text \hfill
will give you a centered column of text, since the column specification not only included the left/right alignment but also that the meterial is set as mathematics. It is probably best to create a separate command to provide this construction, which may then be used anywhere in an alignat, align or similar enviroment, at the beginning of a cell:

\documentclass{article}
\usepackage{amsmath}
\newcommand{\ditto}{{''}}
\newcommand{\ccol}[1]{\omit\hfill #1\hfill}
\begin{document}
\begin{alignat*}{3}
&E&\quad&\ccol{par}&\quad&\Sigma,\\
&\Psi&&\ccol{\ditto}&&\frac{\epsilon V}{1+4\pi\epsilon F},\\
&\Psi&&\ccol{\ditto}&&\frac{(1+4\pi\epsilon F)^2}{\epsilon}.
\end{alignat*}
\begin{align}
E &= mc^2\\
F &\ccol{is another quantity}\\
G &= u^2 + v^2 - w^2 + x^2 - y^2 + z^2
\end{align}
\end{document}
Sould you wish to span multiple columns the relevant command is \multispan, e.g. \multispan{3}\hfill text \hfill will place text spread over three columns and centered.
Alternatively, as Harish Kumar suggests you can use array or tabular:

\documentclass{article}
\usepackage{amsmath}
\newcommand{\ditto}{{''}}
\begin{document}
\begin{equation*}
\begin{array}{r@{\quad}c@{\quad}l}
E&\mathrm{par}&\Sigma,\\
\Psi&\mathrm{\ditto}&\displaystyle\frac{\epsilon V}{1+4\pi\epsilon F},\\
\Psi&\mathrm{\ditto}&\displaystyle\frac{(1+4\pi\epsilon F)^2}{\epsilon}.
\end{array}
\end{equation*}
\begin{center}
\begin{tabular}{r@{\quad}c@{\quad}l}
\( E \)&par&\( \Sigma, \)\\
\( \Psi \)&\ditto&\( \displaystyle\frac{\epsilon V}{1+4\pi\epsilon F}, \)\\
\( \Psi \)&\ditto&\( \displaystyle\frac{(1+4\pi\epsilon F)^2}{\epsilon}. \)
\end{tabular}
\end{center}
\end{document}
However, the default line spacing from alignat is better and you don't need to worry about adjusting the math styles.
arrayor eventabular? – Oct 04 '13 at 07:58\mathrm{''}'s? – daleif Oct 04 '13 at 08:21