I have no problem with your code. Inserted
\hfill
to fill gap between figures of the same row. Below is what I did with different figure packages:
First: deprecated package-
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{subfigure}
\begin{document}
\begin{figure}[ht!]
\begin{center}
\subfigure[$k$~$=$~0.1]{\label{fig:1}\includegraphics[scale=0.4]{Fig1}} \hfill
\subfigure[$k$~$=$~0.5]{\label{fig:2}\includegraphics[scale=0.4]{Fig2}} \\
\subfigure[$k$~$=$~1.0]{\label{fig:3}\includegraphics[scale=0.4]{Fig3}} \hfill
\subfigure[$k$~$=$~2.0]{\label{fig:4}\includegraphics[scale=0.4]{Fig4}}
\end{center}
\caption{Plots.}
\label{fig:Figs}
\end{figure}
\end{document}
Second: with subfig package
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{subfig}
\begin{document}
\begin{figure}[ht!]
\begin{center}
\subfloat[$k$~$=$~0.1]{\label{fig:1}\includegraphics[scale=0.4]{Fig1}} \hfill
\subfloat[$k$~$=$~0.5]{\label{fig:2}\includegraphics[scale=0.4]{Fig2}} \\
\subfloat[$k$~$=$~1.0]{\label{fig:3}\includegraphics[scale=0.4]{Fig3}} \hfill
\subfloat[$k$~$=$~2.0]{\label{fig:4}\includegraphics[scale=0.4]{Fig4}}
\end{center}
\caption{Plots.}
\label{fig:Figs}
\end{figure}
\end{document}
Third: with subcaption package - little modification is made here to OP's code to remove redundancy string
\documentclass{article}
\usepackage[demo]{graphicx}
\usepackage{subcaption}
\begin{document}
\begin{figure}[ht!]
\begin{center}
\subcaptionbox{$k=0.1$\label{fig:1}}{\includegraphics[scale=0.4]{Fig1}} \hfill
\subcaptionbox{$k=0.5$\label{fig:2}}{\includegraphics[scale=0.4]{Fig2}} \par
\vspace{0.5cm}
\subcaptionbox{$k=1.0$\label{fig:3}}{\includegraphics[scale=0.4]{Fig3}} \hfill
\subcaptionbox{$k=2.0$\label{fig:4}}{\includegraphics[scale=0.4]{Fig4}}
\end{center}
\caption{Plots.}
\label{fig:Figs}
\end{figure}
\end{document}