Departing from the US, the old United would never ask for a passport if you check-in online (where you enter your passport number). With the new CO-dominated United (post March 2012) they asked for my passport in the SEA lounge (and stamped my BP) and I think the time before that they asked to see it at the gate.

Departing NRT they asked to see your passport at the gate pre and post March 2012.