The last version of Jet Grind Radio I played was back at the Tokyo Game Show, where it was known as Jet Set Radio. It was definitely one of my favorites of TGS, and it's one of my favorites of E3, also. Of course, now that I can actually read and understand what the characters are trying to tell me, the game has become significantly easier.
The characters have been given names. The main character is called Beat, and his partners in crime are named Gum and Soda. The object of the game is fairly simple - go to all the arrowed surfaces in the level and tag them with your spray paint. To facilitate your illegal exterior design habit, you'll have to collect spinning paint cans that litter the level. After a while, cops will be dispatched to find you and beat the living crap out of you. Evade the man for a long time, and a SWAT team will show up to sling cans of tear gas your way.
Jet Grind Radio will interface with the Dreamcast camera, letting you create your own graffiti decals, snap them with the camera, and import them into the game. Aside from all the spraypainting, there's also a fairly simplistic trick system in Jet Grind Radio. The tricks are mostly based around - you guessed it - grinds. Jumping out of grinds lets you pull off a collection of spins, twists, and flips. The game is very easy to pick up and play, as it only uses three buttons - one to jump, one to paint, and one to dash forward.
Overall, Jet Grind Radio seems to have a widely varied and interesting package, and it also looks like one of the best games here at E3.