Emulation Nation

Links to Emulators

Desmume: Best DS emulator currently available
http://www.desmume.com/

visual boy Advance: Probably the best GBA Emulator available right now.
http://vba.ngemu.com/downloads.shtml

If you're playing on PC, those should be all you'll need.

However, if you're on Droid, here's some other options
 NDS4droid: DS Emulator. Support is limited right now, and the games run pretty slow, only averaging 16-20 fps. However, with updates constantly rolling in, we might see better support in the future. Keep your eye on this

My Boy! Free: GBA emulator that does not support save states in the free version. However, since pokemon has a built in save feature, there's no problem!