If you are flying with a major airline, sign up for their flight paging service, then you will get a phone call, e-mail, page, your choice with the arrivial and departure information.

It's always changing, so it's not like you can make a guess bases more then a few hours out.

Another option to at least see if there is a pattern, is to check the flight status on the airline's website every day, and see if there is a set of gates they use more then others.

Flight paging is the best way if you have a cell phone, you get your arrivial and departure gate information for a connection as you are taxing to the gate (assuming you are on an airline that lets you turn on your cell phone right after landing), check the terminal map in the magazine, and you know if it's a right or left off the plane.