Vicky the Viking: Part 2

DeSmuME is the most advanced, reliable, feature-rich and open-source 100% free Nintendo DS emulator for Windows, Mac, and Linux with ports and forks that work on Android, iOS iPhones and iPads without requiring Jailbreak of iOS devices. It lets you replay all your favourite NDS games from the past for free .

melonDS aims at providing fast and accurate Nintendo DS emulation. While it is still a work in progress, it has a pretty solid set of features:

A multi-system frontend that supports dozens of retro console and handheld cores including NES, SNES, N64, Game Boy, and more.

DS Firmware + (American) DSi NAND And Firmware