You could use the ragged2e package and its command \RaggedRight to make the lines left-aligned. To create a paragraph that's both centered and has a smaller overall textwidth than the surrounding text, you could use the center and minipage environments. In the following MWE, the default width of this environment is 0.6*\textwidth.
\documentclass{article}
\usepackage{ragged2e,lipsum}
\begin{document}
\begin{center}
\begin{minipage}{0.6\textwidth}
\RaggedRight
\lipsum[1] %% filler-text
\end{minipage}
\end{center}
\lipsum[2] %% more filler-text
\end{document}
Addendum: If you have need to create several of these centered-raggedright paragraphs, it's helfpul to create a separate environment, say centragg, for them. The following MWE illustrates how to set it up and how to use it. Note that the centragg environment has a default width of 0.75\textwidth, but this can be overridden by specifying an explicit width, such as 5cm. In addition to invoking \RaggedRight automatically, it also adds a bit of extra inter-paragraph spacing in case there's more than 1 paragraph at a time in the centragg environment. (Traditionally, paragraphs that are typeset ragged-right have no special paragraph indentation.)
\documentclass{article}
\usepackage{ragged2e,lipsum}
\newenvironment{centragg}[1][0.75\textwidth]{%
\begin{center}
\begin{minipage}{#1}
\RaggedRight \setlength{\parskip}{0.5\baselineskip} \noindent\ignorespaces}
{\end{minipage}\end{center}}
\begin{document}
\lipsum[2]
\begin{centragg}
(Default width) \lipsum[2] %% filler-text
\end{centragg}
\begin{centragg}[6cm]
(5 cm wide) \lipsum[10] %% filler-text
\end{centragg}
\lipsum[11] %% more filler-text
\end{document}
The only (?) downside to this approach is that LaTeX will not break minipages (or parboxes, for that matter), across pages, risking an overfull page should the centered paragraph be longer than just a few lines.
\raggedrightinside aquoteenvironment? – lockstep Sep 09 '11 at 16:05