One of the best GBA and NDS emulators out there, it's also the smallest one. Just 115Kbytes and you're ready to play! Does NOT requires DirectX, and it's coded in hand-tuned x86 assembler, so it's heavily optimized to run fast even on older machines. It supports savestates, backup RAM, cable link, and even connection with the real console. Now with *partial* NDS support! It is now one of the best DS emulators around, with an accurate 2D core and a 3D core that's becoming more accurate and fast all the time.
NOTE: There are several versions: the free with NO debugger, the "shareware" for hobby coders ($15), and the Professional edition, with a powerful debugger and lots of development enhancements ($1500 for a site licence!)