As for non-game apps, all there is of significance to download is Nintendo Video and Netflix.
As for games, first there are a number of Virtual Console games of classic Game Boy, Game Boy Color, NES, and Game Gear titles, including many of the best titles for those systems. A few NES games were slightly modified to include 3D effects, these are listed as "3D Classics".
Then there is DSiWare. These aren't 3DS only, but can also be purchased on a DSi. There are a number of those I'd recommend including Alpha Bounce, Mario vs Donkey Kong: The Minis March Again, Shantae: Risky's Revenge, Starship Defense, and the ArtStyle series of puzzle games (especially PictoBits.) There are some other good titles as well that I'm not familiar enough with to recommend.
Many of the retail released games are also available as a download instead a game cartridge. I'll forbear from giving a big long list of those, as there are a lot of good ones.
Lastly, there are some download only titles just for the 3DS. I'd recommend Pushmo, Crashmo, Dillon's Rolling Western, Unchained Blades (which was a retail game as well in Japan but not the US, and is actually a port of a PSP title), Mighty Switch Force, Denpa Men, VVVVVV, and Mutant Mudds. There are a few others I've heard people praise but I haven't played myself.