DeSmuME is the most seasoned open source Nintendo DS emulator. It sports tools designed for hackers, speedrunners, youtubers, and casual gamers. Homebrew programs are supported and can even be debugged through GDB.
The Windows and OSX versions are both relatively feature rich, and there is a small universe of forks and mods that add even more features for casual gaming.
DeSmuME is the origin of RetroArch and OpenEmu Nintendo DS support and is used by several mobile Nintendo DS emulators, with the notable exception of DraStic.
For some reason, this will not load any of the games I try to load. They are games recommended for this emulator, yet so far only Harvest Moon DS: Cute and Rune Factory have loaded, and that was when I first downloaded it. It stays a blank screen with no audio, like before you even try to load any games.