What's almost amazing as the depth of the song itself is the sheer number of adaptions and parodies made to the tune (scroll down a little on the linked page for the list). Some of them have just used the (admittedly catchy) tune, but others have continued to use the history theme, and some of them have been fairly impressive. Here's a list of the three most impressive random histories I've seen set to Billy Joel.
Singapore (a.k.a "I Live in Singapura")
This song is the epitome of a random history. I didn't know anything about Singaporean history until this video, but this song and video were hilarious anyway. And while the song is still funny even in a vacuum, a little context can go a long way in making the video even better.
Political Scandals (a.k.a "We Didn't Start Satire")
This one is a pure song. The video helps with some context, but the song is the real humor here. It outlines almost every political scandal in Washington (and some in other states as well) starting in 1981. This was written for the 30th year of Capitol Steps, a satire group from DC, and their knowledge shows.
Video Games (a.k.a "The Wii Didn't Start the Fire")
This is definitely my favorite song and video on the list. These guys did a great job with the lyrics (which cover the history of video games from their beginning until about 2010), the sound effects (they frequently use sound clips from the things they're referencing, which are awesome if you recognize them), and the video (which uses video clips from virtually everything they mention). They even kept the video in a similar style to Billy Joel.