Humans are optimized for gravity environments, and don't take too well to being without it. Short term side effects can include nausea, vertigo, headaches, and general lousy feelings. Long term, the lack of stress on bones and muscles can cause serious and (at least in the case of bones) possibly irreversible decay in these critical structures, making re-adaption to Earth-normal gravity difficult. While in space, redistribution of fluids can cause balance issues, decrease the ability of the human body to taste, and weaken the immune system. Thus, artificial gravity is probably going to be required for long-term space habitation, hence its inclusion in many science fiction novels (not to mention that in the case of visual media, it makes filming things a lot easier). Perhaps the best example in hard science fiction is the internal centrifuge on the Discovery from the film of 2001: A Space Odyssey.
|USS Discovery Internal Centrifuge, 2001: A Space Odyssey|
Image Credit: Atomic Rockets
There are four major variables in the generation of centrifugal gravity: radius of spin, rate of spin, acceleration generated, and tangential velocity. Because of the mechanics of the problem, knowing values for any two are enough to calculate all four, and online tools like SpinCalc, created by Theodore Hall, exist to do so. These parameters all play a role in human adaptability to the generated spin gravity environment. A shorter radius of spin creates a greater change in gravity level between the head and the feet, due to the height of a human standing on the rim/floor of the centrifuge making up a larger fraction of the radius. Faster rates of spin may create negative physiological effects from the cross-coupling of head motions with the spin of the centrifuge. Non-Earth-normal centrifugal gravity levels may also have long-term negative effects, with <1g environments possibly not providing full protection against the negative effects of weightlessness (though the exact minimum value is not known). Finally, if the tangential velocity of the centrifuge is too low, crew movement inside the centrifuge will cause large variation in apparent gravity. For example, Skylab astronauts were able to create a degree of temporary artificial gravity by running around the "racetrack" of their stationary cylindrical station as can be seen at about the 20 second mark in the video below (inspires an odd sense of deja vu when comparing to the Discovery, above, actually). If they could create some degree of artificial gravity in a non-rotating station (based on timing the jogging in this video, the effective gravity he's creating is maybe about the same as lunar gravity), an actual centrifuge's apparent gravity could be diminished or increased by rapid movement of the crew about the circumference of the centrifuge unless it's tangential speed is great enough.
|Skylab Athletics Video Link|
The maximum acceptable rate of rotation has been studied extensively in ground-based studies, which seem to agree that 3 RPM is a good value for easy adaptability, with rates as high as 6 or 10 RPM maybe being possible with adaption time and low-susceptibility subjects. Similarly, values for tangential velocity can be estimated by looking at the speeds crew may move around inside the centrifuge: If Dave wants to jog around the centrifuge at 2.5 m/s and yet not feel a major reduction or increase in gravity (depending on direction), that allows calculation of acceptable minimum tangential velocity. However, there is not much data on the minimum acceptable gravity loading to ward off the negative effects of prolonged weightlessness, nor on the minimum spin radius that is possible before head-to-toe gravity gradients become an issue, and none at all on prolonged exposure to different levels, or of exposure to intermittent levels of gravity (for instance, spending half the day in 1g or 1/2 g or 1/3 g conditions and the rest in weightlessness). A centrifuge module was planned and partially constructed for ISS with a 2.5-meter-diameter centrifuge, which could have allowed some data about this to be gained from testing on rodents or other subjects, but it was cancelled due to ISS cost over-runs and Shuttle flight scheduling issues.
Because of this lack of data, even NASA reports on the topic of artificial gravity must baseline for 1g, because no data exists on acceptable minimum velocities. Such a level of gravity requires either a large radius (at 4 RPM, a 56 meter radius is required) or accepting the penalties that come with an increase in rotation. Thus, I believe flying some kind of >2m-diameter centrifuge (similar or greater than the original ISS centrifuge module) either to ISS or as a free-flying unit should be a goal undertaken to enable future development and exploration of space.
Even without this data, there are considerations relevant to the design and use of centrifuges that can be discussed by looking at some assumptions and possible near-term space programs, but this post is long already, so I'll leave it for another time. Thus, I'll close with this video, which seems appropriate to the topic at hand.