I saw this on Family Guy a couple of weeks ago and I just now researched to see what the original footage was from. It's from a 1945 movie called, "Anchors Aweigh" and features Gene Kelly and Frank Sinatra and - of all cartoon characters - "Jerry Mouse" from Tom and Jerry.
...and yes, Jerry talks in this movie.
Here is the original footage from "Anchors Aweigh":
And here is the Family Guy clip with Stewie and Gene Kelly:
One thing I like to point out is how green the background is in the original footage. Compare it with the Family Guy video and you can see how some of these old films (before restoration, mind) were in real disrepair.
EDIT: Here's a quick bit of triva from IMDB:
When the dance sequence with Gene Kelly and Jerry the Mouse was screened for MGM executives, someone noticed that although Kelly's reflection shone on the floor during his dancing, Jerry's did not. So all the animators who worked on the sequence had to be rehired to go back in and draw Jerry's reflection on the floor as he was dancing.
Man, that's a lot of work.