Sonic bounces around surprisingly fast. The lack of Spin Dash makes the strategy a bit different from that of Sonic the Hedgehog 2 and Sonic 3 & Knuckles runs, since preserving your momentum becomes a lot more important. However, this doesn't prevent the authors from achieving crazy velocities even with such a significant limitation. In this run, the game is completed while collecting all 6 Chaos Emeralds.
There are also runs where Knuckles and Tails take advantage of their own abilities to finish the game in record time.
The second encode link leads to a camhacked version. But don't expect the videos where Sonic is visible offscreen to make any more sense than the original ones!