Earth vs the Moon, Mars and maybe an atmospheric Venus base, triggered over exploitation of lunar resources by multi-planetary corporations, with insufficient compensation, lack of political representation and poor living conditions resulting in an interplanetary terrorist attack that triggers an overwhelming backlash.
I'll take a potshot and predict it in the 23rd century.
Just a hunch, but it seems to me that in an event to be called WW3 there would be a lot of infighting. There just appears to be a lot more civil unrest in recent decades, and I just have a feeling it would be a war much more fragmented than the ones before it.