“Singin’ in the Rain” performed by Gene Kelly in the film Singin’ in the Rain (1952)
More info on the film on IMDB.com, which is an excellent resource for film. http://www.imdb.com/title/tt0045152/
In this clip, someone has taken a scene from Moulin Rouge! comprised of lyrics from various songs and put in a new audio track so that we can now hear the songs whose lyrics are being excerpted. Remember that this technique of creating something entirely or mostly from other sources is called pastiche. (It is accurate to use the word for both the film and this clip.)
“Diamonds Are a Girl’s Best Friend” performed by Marilyn Monroe in Gentlemen Prefer Blondes (1953)
More details about the film on its page on IMDB.com: http://www.imdb.com/title/tt0045810/
“Smells Like Teen Spirit” - Nirvana
“Material Girl” - Madonna