Well it isn't exactly a sphere - but a rotating vertical circle of RGB LEDs that gives the illusion of a sphere. Nevertheless this project by the folks at Solderlab in Germany is outstanding. Forty RGB LEDs mounted on the ring are driven by a bunch of 74HC595 shift registers via an ATmega328 with Arduino bootloader. Furthermore the Arduino sketch and hardware design files have been provided so you can recreate your own. Or if you just want to experiment they've also published a software simulator of the sphere.
If you're interested in three-dimensional LED displays but not up to making one from scratch, check out our new CUBE4: RGB LED cube kit:
It's easy to construct and use, and with an onboard Arduino-compatible board the cube can be used to display all sorts of data or create visual effects. For more information and to order, visit the CUBE4 page.