I agree it's all subjective, I'm taking the term "upset" not as someone who deserved to win and didn't win, but someone (or something) that everyone expected to win and didn't.
Definitely the 2006 race (I believe it was 2006, might have been 2007, too lazy to check) with Esparza vs. David Hyde Pierce was a shock, most everyone had predicted Raul Esparza would win the Tony since it was announced that COMPANY would indeed be transferring to Broadway. Even when CURTAINS opened, most people thought Esparza was gonna win...and then he didn't. Esparza's face when he lost was the subject of many threads for the rest of the year.
I'd say Scarlett Johannson winning was a bit of an upset, most people were predicting Jan Maxwell to win since she was double nominated that year and she was not gonna win in the lead category.
I also remember a lot of people predicting DOUBT would win Lead Actor in 2004, Bill Irwin looked pretty surprised when his name was announced.
"Some people can thrive and bloom living life in a living room, that's perfect for some people of one hundred and five. But I at least gotta try, when I think of all the sights that I gotta see, all the places I gotta play, all the things that I gotta be at"