Follow the Fleet was a hit film in 1936, but not because of its plot. Plot and acting aside, the film featured a series of awesome song-and-dance routines in which Fred Astaire and Ginger Rogers danced their hearts out. Many of those songs went on to be hits on the radio. Here's my favorite, a performance of "Let Yourself Go" (the song is by Irving Berlin). Are you ready to smile? Okay, go:
If that's not enough for you, here's a tap number from the same film. The actual dancing starts around 2:15; at about 3:40 we see what looks to me like an early version of The Robot.
And here's "Let's Face the Music and Dance," the number that closes the film.
For a longer clip of the "Let Yourself Go" dance number, see this video, and there's also a brief solo Ginger Rogers dance to the same song (apparently it's her only solo dance in her films with Astaire).
If you want to see more of this pair dancing together, TCM released a collection of their work together -- and YouTube is crammed full of clips.
(Via The Kid Should See This.)