In 2001, a review of the literature tried to answer this question.
The study looked at many previous efforts to link laughter and good humour to analgesic effects, immune response and self-reported health.
In short, it found the results inconclusive, inconsistent or negative and the methodology lacking. It makes recommendations into how future trials could be better run.
From the abstract:
Empirical evidence for beneficial effects of humor and laughter on immunity, pain tolerance, blood pressure, longevity, and illness symptoms is then summarized. Overall, the evidence for health benefits of humor and laughter is less conclusive than commonly believed. Future research in this area needs to be more theoretically driven and methodologically rigorous.
From the conclusions:
Taken together, the empirical studies reviewed above provide little evidence for unique positive effects of humor and laughter on health-related variables. [...] In conclusion, despite the popularity of the idea that humor and laughter have significant health benefits, the current empircal evidence is generally weak and inconclusive. [...] this review does indicate that attempts to promote the therapeutic use of humor for purposes of improving physical health are premature and unwarranted by the current research evidence.