[Jacqued]

Well the Dreamcast was a very early gaming console (1998, even the PS2 is from 2000) so obviously only a few games were developed with online gaming in mind (although a lot of them boasted online features like rankings or bonus content). Still, I have very fond memories of online sessions on Chu Chu Rocket, Phantasy Star Online and Quake III Arena. I believe this predates any other initiative of console online gaming by at least a few years.

Maybe I'm a little biased (because nostalgia, and Jet Set Radio), but I think the Dreamcast was ahead of its time by a margin