Question: I noticed that when I play DS games on my 3DS, the games don't fill the entirety of the top screen on the 3DS - there are black bars on either side of the image.

Is there a way to get the game to fill the entire screen? Or is that just going to make things look terrible?

Answer: 
There appears to be two modes for playing DS games on the 3DS. If you hold Select+Start while the DS game is loading, it will display in it's "[Native Resolution](http://www.kotaku.com.au/2011/03/how-the-3ds-alters-ds-games-and-what-you-should-do-about-it/)" on the 3DS screens. 

Unfortunately, this is going to make the black bars bigger and not smaller. As far as I can tell, this is the only other display mode that the 3DS supports when playing DS games. 

It has to do with the different resolutions/aspect ratios of the DS and the 3DS. Similar things happened when playing GB games on the GBA.
Nope, not that I know of. The only way for you to play the DS games is with the format it gives you.