I remember traveling in the 1970s and 1980s, when no one could reliably answer this question until the plane actually left the runway. But today I'm at O'Hare while snow is falling, and it looks like my flight will in fact take off on time despite the snow and the lengthening list of delayed flights on the arrivals board.
How do I know?
First stop is the American Airlines website. Their flight status tool says my plane departs on time from gate K5. And the page has a link to "arriving flight information," which tells me that the plane I'm on will land in 10 minutes.
Oh, really? Yes, really, as Flight Aware's real-time tracker shows me. At this moment, the airplane taking me to San Francisco is heading straight for the O'Hare VOR about 70 km away. (It's over Joliet—no, wait, now it's over Naperville!)
The airline has done it right. By providing real-time information, they're putting me at ease. Even if the incoming plane were circling over Springfield, that would still help me by letting me plan how long I can sit here working before I have to schlepp to the gate.
Update: In the time it took to write this entry, my plane has arrived, and I can see it taxiing towards me right now. I am not making this up. That's not my plane, by the way. That's a plane being de-iced, to show you why I might be a little on edge about my actual departure time today.