Apple has a pretty strict stance on emulators in regards to the App Store, so unless you're willing to jailbreak your iPhone or iPad, the options for retro gaming are usually pretty slim. That is, unless the developers of said apps decide to ignore the App Store entirely -- that is the case with NDS4iOS, a Nintendo DS emulator from the same team that launched the jailbreak-free GBA emulator, GBA4iOS, to much acclaim.
Much like its predecessor, NDS4iOS can be downloaded straight from the official website. After some finagling with the date, which is required since Apple predictably revoked the dev certificate, the app will load up and present an empty list for game ROMs. You can tweak settings like the opacity of the controller overlay as well as frame skips and other performance enhancements.
When you're ready to play, you can seek out game ROMs (to games you already own, of course) via the built-in site links, which then download directly to the app or to a synced Dropbox account. Loading a game is instantaneous and the game provides save state functionality to resume previous play sessions automatically.
Perhaps the best part about the app is that it features full touchscreen support for the "bottom screen" of DS games, offering a true DS experience without the system itself. I found that some games seem to suffer a bit in the transition, however, such as the unexpectedly laggy Mario Kart DS. Other games work splendidly, so it's really a bit of a crapshoot.
If you're thirsty to relive your DS glory days, this is as good as it gets without dragging out your dusty Nintendo handheld and trying to remember where you left the charging cord.