In order to better understand the range of dynamically long-lived giant planet systems, we present the results of a set of bottom-up numerical simulations designed to generate plausible giant planet systems from a large number of planetary embryos. Our simulations produced systems that are stable for at least a billion years and that exhibit a wide range of characteristics. Some of these systems are reminiscent of the outer solar system. The number of planets ranged from one to seven. Many systems contained only Uranus-mass objects. We constructed systems that were more compact than the outer solar system and systems that were much sparser, with planets on very eccentric orbits. Perhaps most surprisingly, some of the systems that we constructed were stable for at least a billion years despite undergoing macroscopic orbital changes on much shorter timescales.