Xbox360 might not be the most important console out of ALL consoles, but I think it's the most important _modern_ console. Online gaming, online store, an indie game channel with XNA (which itself was revolutionary, even though some of its importance might be forgotten today), HD support. A lot of things it got right back when these were all brand new on a console. Plus it had geometry wars.
Geometry wars was very fun. I played on PC always trying to top my friends high scores.
It was the first system of a modern design in a lot of ways.
Six hardware threads, so the thread per subsystem model didn't really work. Instead you got the best results from a DAG of tasks submitted to a job stealing scheduler running on most of the CPU resources. But beside that, no little DSPs that you had to separate work out onto other than the GPU.
And it had the first consumer GPU to incorporate unified shaders (so vertex and pixel shaders ran on the same cores, dynamically scheduled to improve utilization).