It's almost impossible to pin down when and where the first computer animation was created, given several companies and research facilities were dabbling in the new medium at the same time. But AT&T—formerly Bell Labs—and others believe this simple clip dating back to 1963 could indeed be the world's first CG animation.
Not surprisingly, the animated clip isn't exactly a T-Rex dismantling an SUV. Instead, its creator, Edward E. Zajac (who's also narrating), was trying to model and simulate the motions of a satellite orbiting the planet. So the results are basically a wire frame rectangle circling a wire frame sphere—but back in 1963 this was a revolutionary accomplishment.
Programmed in FORTRAN in a time when punch cards were still the norm, and 'rendered' on old IBM 7090 and 7094 computers, the results were then printed—frame by frame—onto microfilm where they could then be watched in real-time via a projector. It's not the most exciting animated adventure, and it's lacking everything from anti-aliasing to motion blur. But back in the day, this was as sophisticated as computer animation could be. [YouTube]