Researchers have studied this one quite a bit. The leader of the pack is James Pennebaker of Southern Methodist University, author of Opening Up: The Healing Power of Expressing Emotions. The National Science Foundation and the National Institutes of Health have helped fund his research. Pennebaker found that people who habitually withhold information about themselves, especially about traumatic events, are much more susceptible to contagious diseases than people who are more open and honest.
One qualification you should know about is that you should only reveal your honesty to people you can trust. But given that limitation, honesty improves your immune system. It’s good for your physical health.