The online adapter for the PS2 is not a modem, it's an ethernet adapter and hard drive. You'll need to have broadband to use it.
It's coming in September or October before the GC and Xbox.
GT3maniac, There are projects in the works to be able to play against different platforms, but they dont work right yet
Iceman, You are thinking or a switch, not a router. A router is used to determnine what direction a packet should be sent.
And finally, do you really think that you could play GT3 over the internet? I think not. This is a game where hundreths of a second count for everything. An arcadey version could work, (i.e. SF rush) but not GT3 as it is. It requires input that is too precise.