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It's difficult to imagine any practical alternatives to spinning that don't require either huge masses or even greater (c^2) concentrations of energy. Large masses aren't a good idea for things that move and to get high enough concentrations of energy you need to start looking at anihilating an amount of mass that would produce G directly, which not only brings you back accelerating lots of redundant mass to move anywhere, but also issues of control and containment.Spinning is cheap and efficient - the only real overhead is that the structure needs to be stressed for it.
And spaceships look way cooler when they're spinning.
Neil, you asked about an "anti-grav" spaceship but I see this has been interpreted, from your lead up comments, as a way of introducing gravity where there is none. Nobody knows how to make "anti gravity" so I will make the same assumption that you mean a means of making artificial gravity. Well spinning is one way and has the advantage that it will keep going in a controlled way with very little energy input. This is good for space stations and for long space flights (say to Mars) with current technology. It is also theoretically possible to create gravity by accelerating at "g" for half your journey, turning round, then decelerating with "g" for the other half. We have not got the technology to do this, but it is theoretically possible. Spinning is the only viable option at present.
In prewar magazines space stations were always depicted doughnut shaped and rotating but I don't think any one has actually been built like that.If gravity is thought as being mediated by Gravitons the impossibility of anti-gravity shields soon becomes apparent, light years of lead are required to stop Neutrinos and Gravitons are postulated as being much less massive.