One of the main reasons Jet Set Radio and its sequel Jet Set Radio Future garnered high acclaim by critics and fans alike are both games' upbeat soundtracks, which featured an array of original and licenced songs of combined music genres such as J-pop, funk, and trip hop to name a few. In this case for both games, it's not so much a Crowning Music of Awesome more than it is a Crowning Soundtrack of Awesome. See also the Sonic Rush Series section in AwesomeMusic.Sonic The Hedgehog, which had music by the same composer. There is now a collected effort to find music in the vein/style of Jet Set Radio here.
Jet Set Radio/Jet Grind Radio
Jet Set Radio Future