Well, no. First off, no. Not in the way Shazam functions where you take your smartphone and have it listen to a song and it tells you what it is, but I think that kind of thing could be getting closer for facial recognition or just plain movie recognition. Anyway, Google Play has added info cards to their Movies & TV app. This means while you're watching a movie on this app, you can decide whether or not you want info cards that tell you things about the film from the actors to the related films to the song that's playing in the background. So it's like Shazam, only Shazam's work has been done for it.
Info Cards on Google Play's Movies and TV App
Here's what it looks like:
The requirements for running this app are that you need to be in the U.S., because we are self-centered jerks, and you need to have a tablet with Android 4.0 on it.
Still, pretty cool feature, and you can turn it off if you just want to enjoy the movie.