Most discussion I have read about using tethers and rotation in order to simulate gravity on spacecraft, talk about simulating Earth's gravity - 1g or 9.8m/s^2.
Baked into the 1g figure is the assumption that humans evolved on Earth where gravity is 1g so it's probably healthiest for us. But is that really necessary? Have there been any studies or research into how much gravity is actually needed in order to minimize the long-term health effects?
A spaceship that rotates to generate 1g of gravity would either require a (debatably) impractically long tether, or have to spin so fast that it would cause a disorienting Coriolis effect. Wikipedia says that the human factors of Coriolis effect would be mostly negligible at 2rpm. By my calculations, At Earth's gravity, that yields a radius of 224 meters, whereas at Mars gravity, that is reduced to 84 meters. One could potentially imagine a spacecraft with two manned modules connected by tethers and a 168 meter long inflatable tube to allow crew and supplies to pass between them; however, bring that up to 448 meters for 1g, that's over a quarter of a mile - and you can see that it starts to become impractical.
A spaceship that is enduring 1g of centripetal acceleration would have to be built with the same rigidity and structural properties of a similarly sized structure on earth, meaning that it would require more materials and therefore have more mass. If we assume the entire craft is assembled on Earth and launched as a unit, Perhaps this is not such a problem - since the spacecraft would have to be built under Earth conditions, and in fact endure acceleration significantly greater than 1g during launch. Even so, the ship would be in a different configuration during launch that could be designed to be more rigid, or perhaps an aerodynamic fairing could be used to provide extra rigidity during launch, or perhaps the acceleration during launch would be on a different axis than the planned rotation. However, assuming some amount of orbital assembly, which is in fact rather likely, there would have to be at least some additional mass overhead to design for 1g of simulated gravity.
If we're going to send astronauts on multi-month or multi-year missions to Mars, or even start a colony there, they're going to be exposed to Martian gravity which is (VERY approximately) one third that of earth. Similarly, gravity on the moon is 1/6 that of Earth. If we think that's OK then why bother with 1g on board the spacecraft to take them there?