That varies culturally and also technologically. People will adapt to very cramped spaces by most of our standards if they have to. OTOH, if your tech supports the equivalent of a nice hotel suite per person instead of submarine quarters, you'll likely do that. Do you have a kitchen and dining space, or can a 'replicator' the size of a microwave oven provide food on demand in most rooms? Theoretically, if the tech is advanced enough and psychological effects aren't a problem, you could keep a man in a 3' x 3' x 7' space quite easily. For long voyages, passengers in suspended animation (including most crew, since their jobs would be intermittent at best during most of the trip as the ship holds course under steady acceleration) might well have such a space (plus probably a bit more for sustaining machinery, of course). At the far end from that, you have the TARDIS, with a potentially infinite interior. In other words, there is no fixed answer.