Think about how old these figures are. If the paint is still tacky so many years later, it's not GOING to dry. It's a chemical problem, a glitch in the manufacturing process. Somewhere I have an email from Ken Lilly that explains what happened, I don't remember all of the technical terms. Browse around here, there are probably already a couple of threads devoted to the problem that go into the causes in more detail.
It depends on what figures, from what series. The wave with Lips is one of the worst. I also had a problem with the shoes on Dr. Phil Van Neuter. Sometimes it's a mild case of tackiness, so you may not have quite the degree of problems I've been describing on Lips.
Another tip for the most severe cases would be to keep them in climate control. Always make sure the temperature and humidity are constant, and try to keep them protected from dust accumulation. Maybe a glass case with doors, or a simple glass dome to go over individual figures. I've seen those at Hobby Lobby in the dollhouse section.
Alex