At what intervals do planes land and take off from Chicago O'Hare?
As a general average, Chicago O'Hare (KORD) seems to do somewhere between 1.5 and 2 operations per minute (so roughly one takeoff or landing every 30-40 seconds).

I based this on data from the FAA's Air Traffic Activity Data System - Terminal Operations report, and specifically looked at November 23 through November 30 of 2014 (17835 operations, over 8 days works out to 1.55 operations per minute - I poked around randomly and found days as high as 1.7 operations per minute).

One of the limiting factors for number of operations at any airport is separation between aircraft, which is covered here


  Incidentally we were discussing airport/tower activity levels in chat earlier today, and Chicago O'Hare is the busiest airport in the United States overall - a title it recently stole back from ATL (which was #1 from 2004 to 2013).