Sonic's stage primarily focused on his incredible speed, and there were tons of straightaways and loops to go through. Sonic still has his traditional spin-dash as well as his spin attack, which can be chained together to fight off multiple enemies. He also has a nice slide attack to use while he's running, although it didn't seem as effective as just jumping up and killing a baddie. Of course, the power slide is a great move to use if you aren't able to react in time.
We also played through a few minutes of Shadow's stage before we died. Shadow controls much like his previous incarnations, although his attacks are really different from Sonic's. For instance, he doesn't have a spin attack in the air. Instead, he fires energy balls at his enemies to obliterate them. Shadow's stage took place in an ancient palace of sorts, but it had an eerie feeling to it, as if we'd played through the stage once before. Take that as you will.

Finally, Silver's stage took place in a tattered cityscape with large robots roaming around. Silver controls much, much differently from his hedgehog brothers. Rather than focusing on raw speed, he uses telekinesis to defeat his enemies. There's an energy meter that you can charge up, and when you have enough power, you can basically lift up anything that's not bolted down. This means Silver can use boulders, rocks, cars and such as weapons of mass destruction.
The game definitely offers some new experiences that haven't been found in the series before, but there are still some issues to be ironed out before the game's release later this year. Most notable is the camera, which gets a little stuck in certain places (up against corners), and sometimes it can't keep up with the action, making it hard to judge the timing of your jumps or attacks. At any rate, Sega is banking on this title to revive the series, which has been stagnant for the past couple of years, so expect any problems, no matter how big or small, to be dealt with before the game's release.