I own an AK2i myself, and I have never encountered a single problem with any game. My game database currently has approximately 196 games, which may not seem like much, but there is quite a bit of ignored games out there, so chances are the games you download could be some of those 196.
The only time I have ever encountered a single error is when I tried modifying the ROM with a program on my computer or combining Cheat codes to where it would corrupt, delete, or hinder with the game's files, etc.
So basically unless it is a homebrew (fan-made, not official) game, I'm pretty sure it can play 95% or more of all DS games.
Just remember that AK2i can not run on an updated 3DS or updated DSi, XL's don't change anything either.