I'll start the ball rolling - one of the duties I cover has 42 four-storey blocks of flats in it, with 22 steps leading up to each storey above ground level so that's 22 times 3 times 42 = 2772 steps ascended.
Obviously there are more steps to be ascended outside the flats but I won't count those. So who's next? Sherpa Tenzing need not post
Edit: a few facts pulled from the web:-
There are 354 steps to get to the crown of the Statue of Liberty, and visitors should plan on a 30 minute climb
The Eiffel tower was an instant success with the public, and nearly 30,000 visitors made the 1,710-step climb to the top before the lifts entered service.
The Burj Khalifa building has 2,909 stairs from the ground floor to the 160th floor.