When looking into maintaining privacy, there are some solutions that are easy to implement (others, though, may be much more difficult). Many of these solutions are compatible with currently existing blockchains, but it depends on what you want to achieve as to whether they are adequate. Technologies that allow users to do absolutely everything on a blockchain without the possibility of being tracked are harder to create.
Such technologies can make your application completely privacy-preserving, allowing your users to benefit from the blockchain's security. In addition, the data is encrypted so that the information and its underlying meaning is completely obfuscated (though the information is computed ...