This is a tough one, because Elvis has so many great songs!!
But the one that immediately comes to mind is the laughing version of Are You Lonesome Tonight - it's a live cut, and when he gets to the spoken bit near the end, he cracks up and can hardlt get the words out for laughing.
It's brilliant, and makes me grin like a loon everytime I hear it.
Here's a link to a version on YT - www.youtube.com/watch?v=NGhmn2i4DBU