I'm leaving today for a 4-day trip with just a backpack (I'm a guy without contact lenses or other medical issues so I need minimal cosmetics) (admittedly I'm taking a bit of a risk by trusting the weather forecast).
A few years ago I went for 10-day trip to Cuba (i.e. you can't really buy stuff there) with a 40L backpack.
A ~40L travel backpack like [1] is legal carryon (and is probably actually a bit more adaptable for overhead space than a typical rollaboard) along with a small laptop bag or other "personal item." It's what I mostly use to travel all over the world for weeks at a time. This is on a regular airline--typically United. I get free checked luggage but rarely take advantage.
A few years ago I went for 10-day trip to Cuba (i.e. you can't really buy stuff there) with a 40L backpack.