I can get this list easily off the website, but it only goes back to March 2010 now. I know I stayed at both Palo Alto properties and the Grand and HR SF properties, for example, so I really have no idea how many unique Hyatt properties I've stayed at. From March 2010, there's 30 unique properties in the list:

48 Lex
Andaz Maui At Wailea
Bellevue
Belmont/Redwood Shores
Boston Harbor
Century Plaza
City Of Dreams Manila
Crystal City
Fremont/Silicon Valley
Grand Denver
Grand Erawan Bangkok
Grand Hong Kong
Grand Istanbul
Grand Kauai
Grand New York
Grand Singapore
Grand Tokyo
Houston
Hua Hin
Manila Casino
O'hare
Park Istanbul - Macka Palas
Park Milan
Park Tokyo
San Francisco Airport
Santa Clara
Schaumburg
St. Louis At The Arch
Union Square New York
Waikiki Beach Resort And Spa