Just to have the pleasure to add something to this discussion:
The US spaceshuttle with the launch rocket can accelerate up to 5g.
Most humans can barely tolerate accelerations beyond 4g, and only for short times.
In hard sci-fi settings (without antigrav stuff), an acceleration of 1g in space could be sustained for extended durations (provided there is enough combustible for the thrusters), if the thrusters actually are "under the feet" of the crew rather than behind their back. This would provide effective Earth gravity. Accelerating at 2g or 3g for long periods would probably be unbearable in the long term.
Now a last guess: we are all used to thrusters in sci-fi, but this is hindering considering acceleration that people and material must endure, especially when you want to reach the speed of light quickly (okay, I know that most Traveller use space jumps). So lets invent a new propulsion system, probably based on gravity manipulation, that affects the whole starship instead of applying thrust to it. As such, everything would accelerate, and not being subject to the effects of thrust while in the starship (and so could sustain 4g, 5g, 10g, or more for any period of time).
Just my 2 g, ahem, I mean my 2 cents.