Were games people, Jet Grind Radio would be an animated girl on crack - and you couldn't resist loving her.
Jet Grind Radio isn't a life altering game. It isn't the greatest platformer ever. (Though I suppose you could say it's the best rollerblading game ever made - given the little competition there is.) But wow, is it an enjoyable one. You've got some character variety, a ridiculously over the top story, and one incredible sense of style.
The style! The cel-shading was phenomenal eight years ago, and it's phenomenal now. It's no wonder everyone was amazed by cel-shading (and understandably with the now decade old Dreamcast) - it really does look good. Jet Grind Radio is simply one of the most visually appealling Dreamcast games. Sure, cel-shading may have turned into a gimmick, and maybe it was a little gimmicky here, but when it fits Jet Grind Radio so well, you can't complain - it's hard to imagine a game like this without cel-shading.
And the music! The music is phenomenal. Fitting right in with the style, the game features a suitably eclectic variety of rock, pop, rap, and the like songs, all sounding suitably enjoyable and catchy (with most being obscure enough that you'll say, "Hey, I haven't heard this song before - and I'm glad I got to experience this song in this life!"). The music, the visuals, and the rest of the sounds in the game are all great quality and all meld together to create one of the most coherent feeling videogames out there stylistically.
All right, so the story's a little bit shallow. It doesn't have any crazy allegory. You don't get to necessarily 'save the world.' You don't get to pick between two arbitrarily exceptionally good and evil moral choices at the end (KotOR/Bioshock). It doesn't even fake you out with the main character 'dying' in some ultradramatic cutscene (when there should be none - Sonic Adventure 2). But beyond that, the story isn't just there for five minutes (pitifully, with the exception of 'storybook' sequences later) just as an excuse to go on some crazy star hunt (Super Mario Galaxy).
The story fits the game. You're some graffiti spraying punk. There are other graffiti spraying punks. You quarrel. You avoid the police. It doesn't need to be complicated, and it's delivered with such style and finesse by DJ Professor K that it's hard to not laugh. (His mouth literally explodes, much like Sonic in the original Sonic Adventure - only in that case, it was strangely disturbing instead of entertaining.)
Sure, the button that controls the camera (meaning it realigns it behind you - the Dreamcast is lacking in the second thumbstick category) is also used to start spraying graffiti - and it sometimes does go behind walls. And there are time limits, yes. (This means you get to respray the graffiti each time you play the level though - a luxury that Jet Set Radio Future doesn't have, and is worse off because of it.)
In the end, Jet Grind Radio is my favorite 'sports' game (not a huge Madden fan), one of my favorite platformers, and just an overall blast to play. It's an excellent experience, and goes highly recommended. It is truly the most playable game on the Dreamcast I've yet experienced.