nds4droid is a free Nintendo DS emulator. It is still in it's infancy but supports many features you'd expect like save states and sound. It also supports the OUYA game console.
The nds4droid FAQ can be found here: http://jeffq.com/blog/nds4droid-faq/
Unlike other DS emulators nds4droid does not not violate the GPL, and it's completely open source.
Unfortunately, Nintendo DS emulation is still somewhat slow, even on higher end phones, but we'll continue to make improvements :). If you're having trouble with performance, try different "frame skip" options.