How to make figure and listing share their counter

You can make things so the figure environment shares the counter with lstlisting. However, you should ensure that lstlisting environments are floating too, otherwise the numbers could not agree and a figure could appear before a listing with a lower number.

\documentclass{article}
\usepackage{listings}

\makeatletter
\AtBeginDocument{%
  \let\c@figure\c@lstlisting
  \let\thefigure\thelstlisting
  \let\ftype@lstlisting\ftype@figure % give the floats the same precedence
}
\makeatother

\begin{document}
\begin{lstlisting}[caption=A listing,float]
a=1
\end{lstlisting}

\begin{lstlisting}[caption=Another,float]
b=2
\end{lstlisting}

\begin{figure}
F
\caption{A figure}
\end{figure}

\begin{lstlisting}[caption=Again,float]
c=3
\end{lstlisting}
\end{document}

Thanks to David Carlisle for noting the need for adjusting \ftype@lstlisting.

If you also want that table shares the counter, add similar instructions.

\documentclass{article}
\usepackage{listings}

\makeatletter
\AtBeginDocument{%
  \let\c@figure\c@lstlisting
  \let\thefigure\thelstlisting
  \let\c@table\c@lstlisting
  \let\thetable\thelstlisting
  \let\ftype@lstlisting\ftype@figure % give the floats the same precedence
  \let\ftype@table\ftype@figure % give the floats the same precedence
}
\makeatother

\begin{document}
\begin{lstlisting}[caption=A listing,float]
a=1
\end{lstlisting}

\begin{lstlisting}[caption=Another,float]
b=2
\end{lstlisting}

\begin{figure}
F
\caption{A figure}
\end{figure}

\begin{table}
G
\caption{A table}
\end{table}

\begin{lstlisting}[caption=Again,float]
c=3
\end{lstlisting}
\end{document}