I learned this mantra from a jet-setting lawyer:
"Checked luggage is lost luggage."
I survived a month in Europe shortly after with carry-ons. It was doable, pleasant even, but I had to make some sacrifices: one pair of shoes, no laptop, no heavy jacket. It's obviously not ideal and possibly not feasible for someone traveling with a non-ticketed baby to travel this way.
It depends on a lot of things (climate, specific personal requirements, etc). My wife & I took our two young children -- 2 and 4 -- to California & Hawaii this summer without checking any bags. It was a 17 day trip. This is way more challenging on business trips when you usually need to pack nicer clothing.
I'm at the end of a 3.5 week trip across Japan and South Korea. One carry-on suitcase, one satchel as my day bag. I can't imagine carrying anything more (though, like you, no kids).
I spent five weeks in India for work last year, one of my coworkers brought an entire suitcase of shoes. He was nothing compared to the guy who brought two overweight suitcases. Our company policy would paid for extra bag fees but not overweight fees. He was pretty pissed when he got hit with those fees by Lufthansa. North of $300 each way out of his own pocket. For the life of me I don't know why he needed so much.
Fringe benefits: since I'm not checking a bag, I can get to the airport a little later. And I also get to leave the airport earlier at my destination since I don't have to wait at baggage claim.
Of course, those of you traveling with kids have it a bit harder, but given the passenger mix on most planes I've flown on, most people could likely follow this advice.