I actually turned down the chance to own two machines that would, if nothing else, be great for usenet dick-waving contests.
A Data General Nova minicomputer.
A Cray. I have no idea what sort of Cray, but it was owned by an institution in York, and needed 3-phase and would have filled my garage. And I had to remove it and move it myself.
I think the oldest machine I've used - at least that comes to memory - is a Compukit UK-101, which actually might not be any older than the Pet or original Apple II. Pongs don't count, otherwise I could go back to '74 at least.
Richard