_An addition (more sweet code) to other answers here._

## Template Name

To just get the current **page template** name, use the following line.

    is_page() AND print get_page_template_slug( get_queried_object_id() );


## File Name

When you just want to echo the **current template file name** got with the following

    /** Plugin Name: Get Template file name */
    function wpse10537_get_template_name( $file )
    {
    	static $name;
    	if ( isset ( $name ) )
    		return $name;
    
    	// Set static var
    	$name = basename( $file );
    
    	return $file;
    }
    add_action( 'template_redirect', 'wpse10537_get_template_name' );

<sup>_This plugin can run as MU-Plugin._</sup>

You can then simply `echo wpse10537_get_template_name()` at any point (in for example a theme template). This avoids cluttering the global namespace.