I hesitate to even give this attention lest the greater internet become an even more unbearable realm, but here 'tis: SoundGifs. Tagline: "communicate using clips from your favorite songs." (Sadly, it seems that you can as of now only play them on the SoundGif site, which kind of defeats the point.)
The idea is (obviously) that the site extracts from SoundCloud files bits and clips of songs that have some particular words that an internet commenter might find funny or interesting to post—yes, in much that same way one might post a normal GIF in a comment thread or wherever. You can search for them by desired lyric extract or just click through the SoundGifs randomly. I did the latter and they started repeating pretty quick.
I guess it doesn't do this automatically at all because the site invites users to make their own SoundGifs, which is pretty easy to do. So there's that.
Songs aren't movies, however, and I'm not sure the GIF idea translates. There's also the whole issue of sound files sounding really horrible when they're abruptly cut-off like this. Implementing a bit of a fade-out would go a long way. Also: embed codes.