The minimum and maximum ages for a health insurance product vary from company to company and are also product specific. While you will need to be at least 18 years of age to buy a health insurance policy for yourself, you could purchase insurance for your children starting almost at the time of birth in some products. You could insure your children through either an individual policy or cover them through family floater policy.
The maximum age for buying a health insurance is typically 60, but some products allow a person to buy an insurance cover upto Age 65.
The maximum age for renewal of an existing policy again depends product to product but most products provide a cover till the age of 70; with some covering till age 80.