Skip to absolute position on line

The already mentioned tabbing package has the disadvantage that it cannot be used across paragraphs, for instance, in itemize environments, as asked in this related question.

However, the tabto package provides exactly what you are looking for via the command \tabto*:

\documentclass{article}
\usepackage{tabto}

\begin{document}
  The quick \tabto{3.5cm}brown \tabto{5.5cm}fox
  \par
  \tabto{3.5cm}jumps too\tabto{5.5cm}far 
  \par\medskip 
  The quick \tabto*{1.5cm}brown \tabto*{3.5cm}fox
  \par
  \tabto{1.5cm}jumps too\tabto{3.5cm}far 
\end{document}

This is what tabbing is for:

\documentclass{article}
\pagestyle{empty}
\begin{document}
\begin{tabbing}
  \hspace*{2cm}\=\hspace*{2cm}\=\kill
  The quick \> brown \>fox\\
\end{tabbing}
\end{document}

Less complicated than Werner's, but using more or less the same idea:

\noindent\makebox[2.5cm][l]{\makebox[1.5cm][l]{The quick}brown}fox

Just as an exercise, here is a different version implementing the idea of backspacing of Dan's comment:

\documentclass[a4paper]{article}
\usepackage{environ}

\newcommand{\startatpos}[2]{\hspace{#1}#2\hfill\cr\ignorespaces}
\NewEnviron{fixedpos}
   {\par\noindent\ooalign{\BODY\crcr}\ignorespacesafterend}

\pagestyle{empty}

\begin{document}
\noindent\rule{1.5cm}{1pt}\par
\noindent\rule{2.5cm}{1pt}\par
\noindent\rule{3.5cm}{1pt}\par

\begin{fixedpos}
\startatpos{0cm}{The}
\startatpos{1.5cm}{quick}
\startatpos{2.5cm}{brown}
\startatpos{3.5cm}{fox}
\end{fixedpos}

\end{document}