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.
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.
nds4droid has potential but sound is not fast enough to be enjoyed and games play is barely fast enough to be considered playable.
Free