Most walk-ups in New York are 5 floors tall. I'm not sure whether this is a zoning standard. The water pressure in the city water mains, however, are just able to reach the fifth floor without the need of an extra pump.
It's always a question for people moving, especially the kids who do it without moving companies: 'What floor are you moving to' and 'What floor are you moving from'? Factor those things in with the time of year, and you can predict what sort of moving day to expect.
I survived moving from a third story walk-up to a fourth story walk-up in July. It was just me and a friend, a van and a cat. The cat did nothing, of course, crouched in her carrier the whole time. The two of us huffed and puffed up and down the stairs, in high humidity, sweat dripping everywhere.
I do recall going to a couple parties at someone's apartment who lived on the seventh floor of a walk-up, somewhere in midtown. To this day I'm not sure how he lived there. What if you forgot to get some milk?
And the craziest thing was that he had parties at his apartment. So all his guests who wanted to smoke had scramble down six flights of stairs to the street, and then hike back up again. It was quite a commitment, those stairs.
Related posts: Looking Up, in Park Slope, On Tenement Life and Cable TV and What's Going Up, Near the ESB.