FlightBoard is a great new app I've been using from the same folks who bring you FlightTrack, my favorite flight-tracking app. With FlightBoard, all you have to do is enter the name of any airport (the app tracks 3991 airports worldwide), and you'll be given the full Departures and Arrivals status of every flight scheduled for that day. You can look at the Departures board, or with a flick of a switch see what flights are scheduled to arrive at that airport.
I really like that all of the columns are sortable - so you can sort by Airline, City of Origin or Destination, Gate number, Departure or Arrival Time, or Flight Status. Click on a flight, and you can instantly send the flight's status by email, as a Tweet, or on Facebook. If you also own the FlightTrack app, you can monitor that flight's status as it comes or goes. The app costs $3.99, which is pretty good for an app with this much info.