My count is 10, with the majority being from Asia (Beijing, Hong Kong MTR and KCR, Shanghai, Shenzhen, Tokyo Metro, and Osaka). I've only been on the TTC, Montreal Metro, and Vancouver Skytrain systems in North America.
I could probably add three more systems that I've been on but are not on the website: Buffalo, the Shanghai airport Transrapid, and a Tokyo commuter train that does not belong to the subway system but very subway-like.
There have been some near misses too: I was close to taking the New York subway, I've been to a Boston subway station, and I was outside a Washington Metro station but didn't go inside (though I really wanted to).