I agree that there is no reserved spaces. I do give a little to the folks in bulkhead rows (Row 1) as, at least on Alaska, they have to put all their luggage in the bins for takeoff/landing as they have no seat ahead of them to store luggage. That is why the FA usually police those more to try and keep them open for travelers in that row. I have never seen someone claim that the bin above their row is "theirs", however and like others have said, putting a bag across the aisle because there is no room on your side is perfectly acceptable, even in Row 1.