Can I download 3DS Games / 3DS ROMs online?
YES - Games for 3DS and NDS can be downloaded form Nintendo RomSites.
Game backup copies or 3DS ROMs are made for playing with R4 3DS flash cards and Nintendo 3DS Emulators. The best compatibility and speed can be achieved using a flash cart, but for those who just want to preview a game on PC before buying it I would suggest a 3DS Emulator. Also Nintendo DS / DSi emulators and nds roms are widely available for free download, and good R4 DS Flash Cards these days cost only around $20 USD, so there is absolutely no reason not to get one for your console if only to play 100% legal homebrew games and applications and enjoy MP3 / DivX / Avi and Comics.