When I was a backpacker, I normally turn up and check-in about an hour before my flights. Now when we travels with our little one, we tend to try to be at the airport earlier to avoid any last minute complications. Furthermore if we take any long-ish flights (over 3 hours) and/or overnight ones, we will definitely try to be at the airport earlier. Most airports such as Singapore’s Changi Airport has children playgrounds. We find it very helpful to check-in earlier and bring our son to spend some time at the playground to tire him out a bit. This will make for a more peaceful flight- he will be tired and fall asleep easily on the flight.
However not many airports are so children-friendly. In fact of the many airports that we have travelled with him in Asia and Europe, the only other one apart from Changi that has anything akin to a children playground is Narita of Tokyo, Japan. I guess it is about time that the new airports should pay a bit more attention to such needs of young parents.