Understanding that it might be difficult to switch packages, even from a deprecated one, here's an update that addresses your requirements.
In order get the sub-figure label to be displayed as a) instead of (a) you have two options:
Either redefine the counter displaying mechanism \thesubfigure. By default, it is defined as
\renewcommand*{\thesubfigure}{(\alph{subfigure})}
which adds the parentheses around the (alphabetic) counter subfigure. Therefore, using
\renewcommand*{\thesubfigure}{\alph{subfigure})}
removes the left parenthesis. However, using only this, you need to accept that text label references to sub-figures will also include this adjustment:

\documentclass{article}
\usepackage[bf]{subfigure}% http://ctan.org/pkg/subfigure
\renewcommand{\thesubfigure}{\alph{subfigure})}% (a) -> a)
\begin{document}
\begin{figure}
\centering
\subfigure[First figure\label{subfig1}]{\rule{100pt}{50pt}} \quad
\subfigure[Second figure\label{subfig2}]{\rule{100pt}{50pt}}
\caption{Some figures}\label{mainfigure}
\end{figure}
See Figure~\ref{subfig1} and~\ref{subfig2}.
\end{document}
or, change the way the sub-caption is set. That is, not mess with the counter representation, but rather the caption setup. This required a modification to \thesubfigure and \@thesubfigure:

\documentclass{article}
\usepackage[bf]{subfigure}% http://ctan.org/pkg/subfigure
\makeatletter
\renewcommand{\thesubfigure}{\alph{subfigure}}% (a) -> a
\renewcommand{\@thesubfigure}{\thesubfigure)\hskip\subfiglabelskip}% a -> a)
\makeatother
\begin{document}
\begin{figure}
\centering
\subfigure[First figure\label{subfig1}]{\rule{100pt}{50pt}} \quad
\subfigure[Second figure\label{subfig2}]{\rule{100pt}{50pt}}
\caption{Some figures}\label{mainfigure}
\end{figure}
See Figure~\ref{subfig1} and~\ref{subfig2}.
\end{document}
Addressing the italic shape of the sub-caption is done using the IT package option:
\usepackage[bf,IT]{subfigure}% http://ctan.org/pkg/subfigure
In general, lower case (old-school) options like bf, it, and sf reference the sub-caption label, while upper case options like BF, IT, and SF reference the sub-caption title/text. See Table 1 (p 6) of the subfigure documentation.
Here is a complete MWE using the above suggestions:

\documentclass{article}
\usepackage[bf,IT]{subfigure}% http://ctan.org/pkg/subfigure
\makeatletter
\renewcommand{\thesubfigure}{\alph{subfigure}}% (a) -> a
\renewcommand{\@thesubfigure}{\thesubfigure)\hskip\subfiglabelskip}% a -> a)
\makeatother
\begin{document}
\begin{figure}
\centering
\subfigure[First figure\label{subfig1}]{\rule{100pt}{50pt}} \quad
\subfigure[Second figure\label{subfig2}]{\rule{100pt}{50pt}}
\caption{Some figures}\label{mainfigure}
\end{figure}
See Figure~\ref{subfig1} and~\ref{subfig2}.
\end{document}
All of the above discussions pertain to sub-figures. However, since subfigure defines an analogous sub-table component, all references to subfigure can be replaced with subtable.
subfigureis outdated, it is superseeded bysubfig. However, you should use packagecaptionby default. It can set nearly everything for the captions. – Jun 29 '12 at 08:53subfigure? – boy Jun 29 '12 at 09:01