Nds4droid is a free Nintendo DS emulator. It’s still new, but it supports many features you’d expect, like saving states and sound. It also supports the OUYA game console.
nds4droid FAQs can be found here: http://jeffq.com/blog/nds4droid-faq/
Unlike other DS emulators, nds4droid does not violate the GPL and is completely open source.
Unfortunately, Nintendo DS emulation is still a little slow, even on more sophisticated phones, but developers are making improvements.
If you are having problems with performance, try different “frame jump” options.
Project website: http://nds4droid.com