One resourceful modder has made a cable that connects the original Gamecube controller to the Nintendo 3DS, and has also got it working with handheld. Some workarounds are involved (head here for more details), also a small cash investment is required. And all this just in time for the release of Super Smash Bros. on 3DS.
In related news, the Wii U version of Super Smash Bros. will get an official adaptor cable from Nintendo, so players can connect the Gamecube controller to the Wii U. You can plug four controllers into the USB device and it will also work with the wireless Wavebird version. Nintendo will also be selling new Gamecube controllers in a bundle with Super Smash Bros. on Wii U, details on that can be found here.