Is there a way to determine if a WordPress plugin is just installed?

Here is the best way I have found so far: (this was written as of WP 3.5)

Info:

The main thing to keep in mind with register_activation_hook is that it is called as a mediary page between clicking an activate link from wp-admin/plugins.php and seeing the Plugin Activated notice after it has been hooked in. I found this out after I tried using the $_GET variable that are sent from the Activate link. If you take a good look the link you click too and the link you end up at are slightly different. This is why you cannot use add_action(), do_action() or add_filter(), .. within the register_activation_hook() triggers. It instantly redirects once a plugin has been activated.

Solution:

You can however use add_option during the hook processes like so

/* Main Plugin File */
...
register_activation_hook( __FILE__, function() {
  add_option('Activated_Plugin','Plugin-Slug');
  /* activation code here */
});

add_action('admin_init','load_plugin');
function load_plugin() {
    if(is_admin()&&get_option('Activated_Plugin')=='Plugin-Slug') {
     delete_option('Activated_Plugin');
     /* do some stuff once right after activation */
    }
}

That should get you started...