In my time I have been on these Metro systems:
From what I can tell the b3co.com website defines a Metro as having an underground rail line somewhere in its train system. Of the Metro systems not acknowledged by b3co.com I've travelled on that of my home city - Melbourne. And I've travelled on city public transport systems that don't (or didn't when I was there) have an underground rail line. Seattle, Den Haag, Geneve, Zurich, and Nice come to mind.
Meanwhile, of those mentioned on the b3co.com website, I'm not sure sure that I have been on both of Metros in New York and Hong Kong; I may have travelled on only one of the systems in each of those cities. And I'm not sure that I've travelled on the rail lines of Tehran and Toulouse; I've certainly been on buses in those cities and the buses may be part of the Metro system, for all I know.
Oh, and I've been on Kuta's 'Transport Mister' service.