Answer: Testicular tumor.
Step 1: A screening test is offered to asymptomatic people to detect a cancer early, so it only pays off when the cancer is common, has a detectable preclinical phase, and a reliable, cheap test exists.
Step 2: The three common cancers listed all have validated screening tools. Breast: mammography (plus clinical and self examination, MRI in high risk). Colon: FOBT, FIT, fecal DNA, sigmoidoscopy, colonoscopy, CT colonography. Prostate: PSA and digital rectal examination.
Step 3: Testicular tumor is uncommon and lacks any cost effective population screening test. There is no recommended screening program for it, so it is the exception. Routine testicular self examination is not endorsed as a screening measure by major guidelines.
Ref: Park's Textbook of Preventive and Social Medicine.