Read Neil Millers article citing the studies

Sample studies:

Albonico et al found that adults are significantly protected against non-breast cancers — genital, prostate, gastrointestinal, skin, lung, ear-nose-throat, and others — if they contracted measles (odds ratio, OR = 0.45), rubella (OR = 0.38) or chickenpox (OR = 0.62) earlier in life. [Med Hypotheses 1998; 51(4): 315-20].

Montella et al found that contracting measles in childhood reduces the risk of developing lymphatic cancer in adulthood [Leuk Res 2006; 30(8): 917-22].