The example environment provided by the covington package is a list environment with the individual items labelled via the equation counter. This does not fit too well with standard solutions to this type of problem: e.g. thmtools works for theorem like environments instead.
The code below uses the tocloft package. However, the standard set-up involves using a new counter. I have chosen to change the counter used by the example environment, so these are now numbered differently from equations.
\documentclass{article}
\usepackage{covington,tocloft}
\newcommand{\listofexamples}{List of Examples}
\newlistof{example}{lex}{\listofexamples}
\newcommand{\lentry}{\addcontentsline{lex}{example}{\protect\numberline{Example
\theexample}}}
\newcounter{examplesave}
\renewenvironment{examples}%
{%
\begin{list}{(\theexample\lentry)}%
{%
\setcounter{examplesave}{\arabic{example}}%
\usecounter{example}%
\setcounter{example}{\arabic{examplesave}}%
\setlength{\listparindent}{0pt}%
\def\makelabel##1{##1\hfil}%
}%
\raggedright}%
{\end{list}}
\renewcommand{\exampleno}{\refstepcounter{example}\theexample}
\begin{document}
\listofexample
\begin{examples}
\item An example
\item Another example
\end{examples}
\clearpage
\begin{example}
Last example
\end{example}
\end{document}

The above code sets up the list of examples mechanism in the standard tocloft way and then provides a new version of the example environment with the equation counter replaced by an example counter at each instance. The labelling command is extended to add an appropriate line to the table of examples via the \lentry command. I have also included a redfinition of the only other command in the covington package that uses the equation counter for examples.
Finally, remember to run latex on such a file twice to get the correct numbering in the list of examples.
covingtonwould change anything. – Scott H. Nov 29 '12 at 7:40