WordPress supports oEmbed, but only in post content. Lame.
If the plugin is active, oEmbed will automatically be on in your comments on the front end. It doesn't have any UI, just activate it and go.
This is "officially" (whatever that might mean) released in the WordPress.org plugins repository as oEmbed in Comments.
WordPress core caches oEmbed results in post meta. Since this plugin uses WordPress core's oEmbed methods, comment oEmbed results get cached in their parents' post meta. If comments with oEmbed media ever get rendered in a context where the
$post global is not the comment's parent, you may end up with weird (but probably not problematic) data in your database. There is an open WordPress core ticket about this.