Is there a simple way to use the gentium font in latex?

Posting the XeLaTeX comment as an answer, per suggestion. You just \setromanfont{Gentium}.

Note that the font Gentium doesn't yet have a bold variant, so if you need to use bold frequently, it's recommended that you use a different font. (If your interest in Gentium is because of its wide character repertoire, you may want to use a font like Charis SIL. If your interest was in the appearance, then there's a "Gentium Basic" that doesn't include Greek or Cyrillic characters, but has bold variants.) But in practice I found I could use Gentium with Gentium Basic Bold as the bold font, and it looks natural to my eyes (you still won't have bold Greek, of course):

\documentclass{article}
\usepackage{fontspec}
\setromanfont[BoldFont={Gentium Basic Bold},ItalicFont={Gentium Italic}]{Gentium}

\begin{document}
Look:\\
Hèllö wőrld: γεντιυμ \textit{Italic} \textbf{Bold}\\
\textbf{Hèllö wőrld}: γεντιυμ \textit{Italic} Bold
\end{document}

If you want to use pdfLaTeX, you can use the autoinst tool.

cd ${YOUR_TEX_DOCUMENT_DIR}
autoinst ${PATH_TO_GENTIUM}/Gen*.ttf

This will convert the ttf files and create a Gentium.sty file in the current directory. Now you can simply

\usepackage{Gentium}

to switch your LaTeX font to Gentium. Alternatively, try GentiumBasic for bold.

Now there is a gentium-tug package that enables you to

\usepackage{gentium}

No additional steps required.