Sunscreen protects against two common forms of skin cancer, squamous cell carcinoma (SCC) and basal cell carcinoma (BCC), and several sunscreen ingredients protect against tumor development in photocarcinogenicity tests in mice. However, there is some evidence, largely arising from correlational studies and in vitro experiments, that sunscreen use may be linked to increased risks of malignant melanoma, a rarer but more deadly form of skin cancer. It has also been linked to Vitamin D deficiency. The broad areas of concern are:
potentially carcinogenic properties of some sunscreen ingredients
Vitamin D deficiency caused by reduced exposure to ultraviolet light
incomplete protection against the full ultraviolet spectrum combined with increased time spent in the sun
This lead to a Sunscreen controversy within the academic community. It is known that some sunscreens only protect against UVB radiation, and not against the more dangerous UVA spectrum. A number of class-action lawsuits allege that sunscreen manufacturers misled consumers into believing that these products provided full sun protection. The vitamin D hypothesis is not as widely accepted but continues to generate scholarly debate. Most health authorities and medical associations have concluded that on the whole, sunscreen use is beneficial, but there is not yet a thorough consensus. ...
Sunscreen ingredients can damage DNA
Some sunscreen ingredients may damage cells when illuminated.   PABA causes DNA damage in human cells. PABA was banned as a sunscreen ingredient several years after these findings were published. Phenylbenzimidazole (PBI) causes DNA photodamage when illuminated while in contact with bacteria or human keratinocytes.
Some sunscreen ingredients generate Reactive oxygen species when exposed to UV-A, which can increase carbonyl formation in albumin and damage DNA. It is also well-known that DNA alterations are necessary for cancer to occur.
Many sunscreen ingredients generate singlet oxygen under illumination. Several popular UV-filters have been demonstrated to generate free radicals.
Kerry Hanson et al. have shown for the three sunscreen ingredients octocrylene, octylmethoxycinnamate, and benzophenone-3 that after the sunscreen chemicals had time to absorb into the skin the number of ROS and free radicals is higher for the sunscreen user than for the non-user. Such an increase in ROS might increase the chance of melanoma, but this hypothesis has not been tested.
DNA, in particular, is susceptible to damage caused by photo-excited compounds.
Personally, I think the best protection is natural protection. Let the body develop a tan slowly. Start in the Spring while the sun rays are still at angle so as not to be so strong. Only stay out for short periods of time at first. In the Summer, limit sun exposure to after 3 PM when the sun rays are at an angle and not so strong.