I would guess that most people, when they take the time to consider how many worlds they live in, would answer “two”. These would be the physical and mental worlds. There is some sort of relationship between what is “out there” and how we sense it and then represent it on our minds. That relationship is complex and subjective. There is also some question about whether we exist in a duality, with mind and body being entirely separate, or in some sort of unified whole where mind and body are one. I suspect that research into brain science may give rise to some new forms of philosophy shortly, or at least some new questions and arguments.
One of the enduring philosophical questions is whether and how the mind can have causal effect on the “real world”. in his 1978 lecture on human values, Karl Popper delves into these questions and adds a new wrinkle. He suggests that we live in three worlds, rather than two.