Denoting the end of example/remark

Try the following indirect method (requires amsthm):

\newtheorem{examplex}{Example}
\newenvironment{example}
  {\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\examplex}
  {\popQED\endexamplex}

In this way also \qedhere works exactly like in proof.

Full example.

\documentclass{article}
\usepackage{amsmath,amsthm}

\theoremstyle{definition}
\newtheorem{examplex}{Example}
\newenvironment{example}
  {\pushQED{\qed}\renewcommand{\qedsymbol}{$\triangle$}\examplex}
  {\popQED\endexamplex}

\begin{document}

\begin{example}
This has only text.
\end{example}

\begin{example}
This has also a display at the end:
\begin{align*}
f(x) &= \bigl( g(x) \bigr) \\
h(x) &= \bigl( r(x) \bigr).\qedhere
\end{align*}
\end{example}

\end{document}

I think this is totally a matter of personal style. If you are using \qed already you could use a similar symbol like \triangle.

Whatever you do, don't just use \hfil$\triangle$ because this does not work when your example fills the last line completely. Here is a definition of \demo that uses the flexible \xqed:

\documentclass{minimal}
\usepackage[utf8]{inputenc}

\newcommand\xqed[1]{%
  \leavevmode\unskip\penalty9999 \hbox{}\nobreak\hfill
  \quad\hbox{#1}}
\newcommand\demo{\xqed{$\triangle$}}

\begin{document}
Lorem ipsum dolor sit amet, consectetur adipisicing elit, sed do eiusmod
tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam.
\demo    
\end{document}

The manfnt font also provides a filled triangle pointing to the right. After declaring \font\manual=manfnt you can use \manual\char'170.

The very useful thmtools package has a key for defining the qed-symbol. For example, I use the following in my documents:

\usepackage{amsthm,thmtools}
\theoremstyle{remark}
\declaretheorem[name=Example,qed={\lower-0.3ex\hbox{$◃$}}]{Ex}

...

\begin{Ex}
  The numbers 2, 3 and 5 are all prime.
\end{Ex}

(I use unicode-math to be able to use the ◃ symbol directly. Just replace it by whatever symbol you like, e.g. \triangleleft.)

Everything is set up correctly so that you can use \qedhere like in a standard amsthm proof environment.