How to remove footline on the title page of beamer slides

You can redefine footline locally for the title frame; I also modified the framenumber counter so that the frames including the footline start from one:

\documentclass{beamer}

\useoutertheme{infolines}
\setbeamertemplate{footline}{\hspace*{.5cm}\scriptsize{\insertshorttitle
\hspace*{50pt} \hfill\insertframenumber\hspace*{.5cm}}\\
\vspace{9pt}} 

\author{An Author}
\title{The Title}

\begin{document}

{
\setbeamertemplate{footline}{} 
\begin{frame}
  \titlepage
\end{frame}
}
\addtocounter{framenumber}{-1}

\begin{frame}
A frame with footline
\end{frame}

\end{document}

Here is solution via the plain option of frame environment (this solution works even with the ignorenonframetext option).

\documentclass[ignorenonframetext]{beamer}

\useoutertheme{infolines}
\setbeamertemplate{footline}{\hspace*{.5cm}\scriptsize{\insertshorttitle
\hspace*{50pt} \hfill\insertframenumber\hspace*{.5cm}}\\
\vspace{9pt}} 

\author{An Author}
\title{The Title}

\begin{document}

\begin{frame}[plain]
  \titlepage
\end{frame}

\begin{frame}
A frame with footline
\end{frame}

\end{document}