How to disable automatic indent?

Before setting \parindent to zero, we can store its value in another length variable and redefine the \indent command to use this other length variable instead of \parindent (which has been set to zero).

\documentclass[12pt]{article}

\newlength\tindent
\setlength{\tindent}{\parindent}
\setlength{\parindent}{0pt}
\renewcommand{\indent}{\hspace*{\tindent}}

\begin{document}

This is some text that will not be indented.

\indent This is some text that will be indented.

\end{document}

For even lazier people. ;)

You can use the parskip package, just add \usepackage{parskip} to your preamble. From the documentation:

Package to be used with any document class at any size. It produces the following Paragraph Layout: Zero Parindent and non-zero Parskip. The stretchable glue in \parskip helps LATEX in finding the best place for page breaks.