A key to maintaining good health is catching problems as early as possible or preventing them altogether. This is the reason for screenings and immunizations. Recommended immunizations for seniors are flu shots (yearly), tetanus shot (every ten years), pneumonia (once) and, if you had chicken pox as a kid, shingles (once).
If you live in the Southwest or spend much time outdoors, annual screenings for skin cancer are in order. Screenings are also recommended for hypertension, COPD, breast, cervix, prostate, and colon cancers.
In addition, regular doctor visits enable you and your doctor to track physical changes and adjust behaviors and medications accordingly. Your doctor can recommend other screenings or more frequent screenings based on your individual needs.
However, if you’ve reached the age where you wouldn’t seek aggressive treatment for a condition, there’s no point in continuing to test for it. (No colonoscopies after age 85, for example.)