At non-hub airports it's pretty easy to do, using the gate information on the arrivals / departures bit of co.com. For example, if I'm in ATL waiting for a CO flight and want to know where it's coming from and where the incoming flight is, I just have to look at EWR/IAH/CLE-ATL flights and see which one is due to arrive at the same gate my flight's leaving from.

At hubs it's virtually impossible however...