wordpress get_template_directory
get_template_directory() returns the directory, but it doesn't echo it.. so if you use it with echo it will work
<img src="<?php echo get_template_directory(); ?>/images/bg.png"></img>
but I will suggest to use get_template_directory_uri() instead, because above will not be portable ( windows use backward slashes as separator )
<img src="<?php echo get_template_directory_uri(); ?>/images/bg.png"></img>