STILL VERY INCOMPLETE
Nintendo never released an official Virtual Console on the DSi, which means that the platform wasn't made portable until 2011 when it was released for the 3DS. But it's about to change.
I'm working together with some DS homebrew developers to make forks off existing emulators for DS, resulting in a brand new custom DSi Virtual Console with restore points, suspend points, custom settings and a brand-new official looking interface. This new DSi VC will be made for use with HiyaCFW and RocketLauncher.
Credit to:
-Gericom for the GBARunner2 emulator
-Drenn for the GameYob emulator
-Loopy for the NesDS emulator
-Yardape8000 for the NeoDS emulator
Special thanks to:
-Apache Thunder, Gericom, StuckPixel, Shutterbug2000, Robz8 and Nocash for HiyaCFW
-The developers I mentioned above for making the emulators
-Apache Thunder for discovering and announcing RocketLauncher