Check if file exists
I don't think it's possible to do with out-of-the-box Twig/Craft, but it's a super-easy plugin to write.

All you'd need is to give your plugin a Template Variable so that you could do:

{% if craft.myAwesomePlugin.fileExists('somePath') %}
    YES
{% endif %}


And your MyAwesomePluginVariable class has a method like:

public function fileExists($path)
{
    return IOHelper::fileExists($path);
}