The Caps didn’t invent the use of Tom Green screaming “Unleash the Fury” to excite home fans. That honor, as far as I know, goes to the Atlanta Thrashers, who don’t technically exist any more.
Still, I think the Caps likely gathered the most attention for their regular Unleashing of the Fury, typically late in the third period of most games. Green Unleashed the Fury in a Caps jersey, and David Gregory Unleashed the Fury, and Pat Sajak Unleashed the Fury, and Karl Alzner said it’s “got to be one of the best things that goes [on] in the league,” and so on.
A friend, however, recently told me that Tom Green had showed up on the big screen in Madison Square Garden, encouraging Rangers fans to Unleash the Fury. Indeed, said friend just forwarded me this video. If you zoom through to about 3:32, you can hear it pretty clearly.