Windows/Mac: DeSmuME is a featured-packed Nintendo DS emulator capable of playing ROMs and homebrew software, one that also offers extra features unavailable on a traditional DS.
DeSmuME emulates all the functionality of the DS including the buttons, touchscreen interface, and even the Wi-Fi connection. You can simply play your ROMs and homebrew apps, but in addition to playback, you can take screenshots, create movies from your gameplay, load cheat codes, and save your game state. That allows you to save any game at any time, even if the game doesn't support profiles or saved games.
DeSmuMe is freeware and available for Windows and Mac. Check out NDS Homebrew for a variety of homebrew games and applications.