It depends on the airport. My home airport is MCI so, sadly, very few international nonstops (except those to Mexico and now Icelandair to KEF). I see no reason to be there 3 hours early for a flight that's going to connect in ORD to an international flight. The only extra work they need to do at MCI is verify my passport.
I do try to allow 2-3 hours if it's an airport where I have to go through "security" AND passport control.