Best way to initiate a class in a WP plugin?

Question

I've created a plugin, and of course being me, I wanted to go with a nice OO approach. Now what I've been doing is to create this class and then just below create an instance of this class:

class ClassName {

    public function __construct(){

    }
}

$class_instance = new ClassName();  

I'm assuming there is a more WP way to have this class initiated, and then I came across people saying that they prefer to have an init() function than a __construct() one. And similarly I found the a few people using following hook:

class ClassName {

    public function init(){

    }
}
add_action( 'load-plugins.php', array( 'ClassName', 'init' ) );

What is generally considered the best way to create a WP class instance on load and have this as a globally accessibly variable?

NOTE: As an interesting side point, I've noticed that while register_activation_hook() can be called from within the __construct, it cannot be called from within the init() using the second example. Perhaps someone could enlighten me on this point.

Edit: Thanks for all the answers, there clearly is a fair bit of debate as to how handle the initialization within the class itself, but I think there's generally a pretty good consensus that add_action( 'plugins_loaded', ...); is the best way to actually kick it off...

Edit: Just to confuse matters, I've also seen this used (although I wouldn't use this method myself because turning a nicely OO class into a function seems to defeat the point of it):

// Start up this plugin
add_action( 'init', 'ClassName' );
function ClassName() {
    global $class_name;
    $class_name = new ClassName();
}