So not to negate what was already said. But even with super accurate integrators, or even perfect math, under the laws of gravity 3 body systems are not stable. There are like 3 exact configurations of 3 body's that are stable as far as mathematics are concerned but perturb them in any way....
Its called the 3 body problem. http://en.wikipedia.org/wiki/Three-body_problem
However in reality there is typically only one important body and the rest can be ignored. For example when considering the earths orbit around the sun, we can even ignore the earths mass and we have approximately a 1 body system with an infinitely light mass orbiting it. When considering earth, moon and sun we can consider earth moon as a system, then the earth/moon center of mass orbits the sun. If we want to add Jupiter to the mix, we ignore the effects of earth on Jupiter etc.
However full simulations are also possible, BUT you do it different from just brute force accuracy. You need the integration method to be reversible to conserve important properties of the system (mostly momentum). So a 2nd order leapfrog is typically way better than a 4th order RK method.
But do you need this accuracy for a game? Using parametric orbits probably works better anyway.