Your plots are too wide. You may try to put 2 plots in a row instead of 3. However, there is always this box techniques that can be used.
\documentclass[]{article}
\usepackage{pgfplots, alphalph}
\usepgfplotslibrary{groupplots}
\begin{document}
\begin{figure}
\makebox[\textwidth]{%
\begin{tikzpicture}[font=\footnotesize\sffamily]
\begin{groupplot}[
group style={group size=3 by 2, vertical sep=70pt,
ylabels at=edge left
},
view={0}{90},
width=5.2cm,
height=5.2cm,
scale only axis,
scaled ticks = false,
tick label style={/pgf/number format/fixed},
title={My title},
xlabel={x-axis},
ylabel={y-axis}],
unbounded coords=jump]
]
\nextgroupplot [title={\it{Title 1}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\nextgroupplot [title={\it{Title 2}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\nextgroupplot [title={\it{Title 3}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\nextgroupplot [title={\it{Title 4}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\nextgroupplot [title={\it{Title 5}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\end{groupplot}
\end{tikzpicture}
}
\end{figure}
\end{document}

If in case, you want to center the last two plots, you may use a suitable width for all plots (so that you know how much to shift) and use xshift like
\nextgroupplot [xshift=1.2in,title={\it{Title 4}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};
\nextgroupplot [xshift=1.2in,title={\it{Title 5}}]
\addplot[black, thick, mark=o, only marks]
coordinates {
};

With table:
\documentclass[]{article}
\usepackage{pgfplots, alphalph}
\usepgfplotslibrary{groupplots}
\usepackage{filecontents}
\begin{filecontents*}{mydata.dat}
A B
1 4
2 6
3 9
4 2
5 3
\end{filecontents*}
\begin{document}
\begin{figure}
\makebox[\textwidth]{%
\begin{tikzpicture}[font=\footnotesize\sffamily]
\begin{groupplot}[
group style={group size=3 by 2, vertical sep=70pt,
ylabels at=edge left
},
view={0}{90},
width=5.2cm,
height=5.2cm,
scale only axis,
scaled ticks = false,
tick label style={/pgf/number format/fixed},
title={My title},
xlabel={x-axis},
ylabel={y-axis}],
unbounded coords=jump]
]
\nextgroupplot [title={\it{Title 1}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\nextgroupplot [title={\it{Title 2}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\nextgroupplot [title={\it{Title 3}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\nextgroupplot [title={\it{Title 4}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\nextgroupplot [title={\it{Title 5}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\end{groupplot}
\end{tikzpicture}
}
\end{figure}
\end{document}
and with
\nextgroupplot [xshift=1.2in,title={\it{Title 4}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};
\nextgroupplot [xshift=1.2in,title={\it{Title 5}}]
\addplot[black, thick, mark=o, only marks]
table[x=A,y=B]{mydata.dat};

tableenvironment in place ofcoordinates? For some reason, this code does not work (yet) withtable {}Please just add a new section to your answer, do not delete anything you have written, it is very useful. – warship Apr 24 '15 at 05:36