Itemize without bullets

You can do this in several ways: for example, by using an empty optional argument for \item (as Jake suggested), or by using the enumitem package to use an empty label, or by redefining \labelitemi; these approaches are illustrated in the following example:

\documentclass{article}
\usepackage{enumitem}

\begin{document}

\begin{itemize}
  \item[] First.
  \item[] Second.
\end{itemize}

\begin{itemize}[label={}]
  \item First.
  \item Second.
\end{itemize}

{\renewcommand\labelitemi{}
\begin{itemize}
  \item First.
  \item Second.
\end{itemize}
}

\end{document}

Why do you want to use the itemize environment, if you don't want the bullets? You could simply use the description environment which seems to be exactly what you need. No hacking required.

\documentclass{article}

\begin{document}
    \begin{description}
        \item Foo
        \item Bar
    \end{description}
\end{document}

The following also works. The {} specifies that nothing should be placed before the items. Use \indent as needed.

\usepackage{enumerate}

\begin{document}

    \begin{enumerate}[\indent {}]
        \item ABC
        \item ABC
        \item ABC
    \end{enumerate}

\end{document}