bloodworks gives the simplest solution. However, if you want to retain exactly the formatting for the title page, but just not have the page number information, then you can redefine the footline template just for that frame as follows:
\documentclass {beamer}
\mode<beamer>{\usetheme{Madrid}}
\title[Test Title]{Test}
\begin{document}
\bgroup
\makeatletter
\setbeamertemplate{footline}
{
\leavevmode%
\hbox{%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
\usebeamerfont{author in head/foot}\insertshortauthor\expandafter\beamer@ifempty\expandafter{\beamer@shortinstitute}{}{~~(\insertshortinstitute)}
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
\usebeamerfont{title in head/foot}\insertshorttitle
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
\usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
% \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}
\hspace*{6ex}
\end{beamercolorbox}}%
\vskip0pt%
}
\makeatother
\begin{frame}
\titlepage
\end{frame}
\egroup
\setcounter{framenumber}{0}
\begin{frame}
\frametitle{First test frame}
\begin{itemize}
\item Item 1
\item item 2
\end{itemize}
\end{frame}
\begin{frame} More \end{frame}
\end{document}

The code makes a local group around the first frame via \bgroup / \endgroup and then contains a copy of the footline template from beamerouterthemeinfolines.sty with the insertion of "frame numuber / total framenumber" commented out and replaced by an appropriate amount of horisontal space.
Had not been for the " / " between these numbers you could just have set the commands \insertframenumber and \inserttotalframenumber to insert a single space each in this group.
After discussion with bloodworks, one may prefer to package the above up in to a macro \mytitleframe as below. Such a definition could then be moved to a private style file.
\documentclass{beamer}
\mode<beamer>{\usetheme{Madrid}}
\makeatletter
\def\mytitleframe{\bgroup
\setbeamertemplate{footline}
{
\leavevmode%
\hbox{%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{author in head/foot}%
\usebeamerfont{author in head/foot}\insertshortauthor\expandafter\beamer@ifempty\expandafter{\beamer@shortinstitute}{}{~~(\insertshortinstitute)}
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,center]{title in head/foot}%
\usebeamerfont{title in head/foot}\insertshorttitle
\end{beamercolorbox}%
\begin{beamercolorbox}[wd=.333333\paperwidth,ht=2.25ex,dp=1ex,right]{date in head/foot}%
\usebeamerfont{date in head/foot}\insertshortdate{}\hspace*{2em}
% \insertframenumber{} / \inserttotalframenumber\hspace*{2ex}
\hspace*{6ex}
\end{beamercolorbox}}%
\vskip0pt%
}
\maketitle
\egroup
\addtocounter{framenumber}{-1}
}
\makeatother
\title[Test Title]{Test}
\begin{document}
\mytitleframe
\begin{frame}
\frametitle{First test frame}
\begin{itemize}
\item Item 1
\item item 2
\end{itemize}
\end{frame}
\begin{frame} More \end{frame}
\end{document}