Advanced Responsive Video Embedder does a very nice job of embedding videos that are responsive and fill their container, which is exactly what I am looking for; and it works with many, many video websites.
With that said, I must add that I would prefer to not use shortcodes for the simple reason that if for any reason I stop using the plugin, every embed would need to be redone (I have 100s of videos). So I will honestly say that for most oembeds (simply placing the url in the post) I use Advanced Responsive Video Embedder. But when I have found videos that don't work with that plugin (iframe embeds in particular), Advanced Responsive Video Emdedder comes to my rescue! It has worked for every site that supports iframe embeds that I have come across.
Than you, Nico, for this great plugin!