To add to the Mario one, Paper Mario 1, 2 and 4 battles are on a stage, with a curtain a la Super Mario Bros. 3, with actual audience (which you actually need in Paper Mario 2 to restore your power gauge, and it even is eatean away by a couple of bosses). When Paper Mario starts, at the intro, a curtain opens and a narrator talks, and when the game finishes, I believe a curtain closes. Also, at the end of Paper Mario 2, there's a scene where they supposedly made a play of Mario's adventure (Yo dawg...), so Mario 3 is not the only game that fits this theory.
Oh, and to defend Super Mario USA a bit, it being a dream doesn't mean it didn't really happen. The world the adventure takes place is called Subcon, and is a world that can only be accessed through dreams, so Mario and co. actually did save a world but they remember it as a dream.