Omitting the date when using \maketitle

If you want a blank date, just use \date{}.

If you want to remove the spacing altogether where the date usually goes, look into using the titling package, or else the mechanisms provided by your document class, depending on what it is.

For a cheap and easy solution to removing the spacing without delving into the titling package that frabjous mentions, try:

\documentclass{article}

\author{Me}
\title{Foo}
\date{\vspace{-5ex}}
%\date{}  % Toggle commenting to test

\begin{document}

\maketitle

Bar

\end{document}

@Reid’s titling solution (mentioned above in a comment, and alluded to in @frabjous’s answer) deserves a full answer, since it does a nice job of removing the space associated with the date:

\documentclass{article}

% remove spacing around date:
\usepackage{titling}
\predate{}
\postdate{}

\author{Author, A.}
\title{Alpha}
\date{} % clear date

\begin{document}

\maketitle

Some text.

\end{document}